I think I see your confusion, and in retrospect, that is somewhat oddly worded given that Location and Dangers aren't really detailed elsewhere. I'm going to start from the root of this, so if one of these sections looks really basic and obvious try skipping to the next section.
Use a monster, danger, or location move
In Dungeon World, the GM is limited in much the same way the players are. When something gives the GM the opportunity to act (usually a player rolling badly) then the GM picks one of the moves from their list. The first of those (and probably the most commonly used) is "Use a monster, danger, or location move." This seems a little strange (we get a move that lets us get another move? What?) but it's exactly what it sounds like. When you use this move, you pick a monster, a danger, or a location, and use one of its moves instead of one of the other GM moves. The narration should be the monster, danger, or location doing something to present a problem.
You are totally allowed to narrate one of the other moves using a monster, danger or location! A monster could laugh and tell them the horde sacked the town last night revealing an unwelcome truth, a storm could get water into the supplies using up their resources, and a cave tunnel could collapse and separate them.
How would a location have moves?
When a location uses a move, it doesn't necessarily mean that the place has a genius loci or other animating mind. If you're making a location up, you can give it moves just like you'd give monsters moves. Except, there's a section in the book talking about how monsters have moves and how to figure out what moves a monster has, and nothing like that for locations. I never actually noticed that until I saw this question. Basically, think of things in a location that would go wrong for the players; in a bog someone might get stuck in the mud, on a mountain stones might crumble underfeet causing someone to fall, in a dungeon there might be traps that fire at the players. Those could all be moves. You can improvise them on the fly from the basic GM moves, but if you aren't a huge fan of improvising you can totally make some in advance. I've made an example below.
Volcanus Peak
(Magma)d8 damage. Tags:Magical, terrifying
Volcanus peak is a less-than-dormant volcano. It's a dangerous place even if there were no death cult intent on seeking the end of all things, but such is the life of an adventurer.
Instinct: To drive out interlopers
- Crumble beneath someone's feat
- Let loose flows of liquid flame
- Erupt in a terrifying display
That's not the best example of a move, but you can see how we're basically building a monster without hit points. (How do you kill a location? If you have an answer to that, by all means give it HP.) It does things the same way monsters do.
Alright, but what's a danger anyway?
You got it in one. When you make fronts, you also make dangers for the front. When you make dangers, you also make a couple of moves for those dangers. Check out the section on making fronts again- they give a whole bunch of example moves for different kinds of dangers (Planar forces, hordes, etc) and even a section on making custom moves if you need them.
TLDR
Basically, in Dungeon World some locations and all the specific dangers of a front have moves just like monsters. When the players give you the ability to make a move (probably by failing a roll, or by standing around looking at you) then you can make a general GM move, or a more specific move of a monster, location, or danger. Monster moves are detailed really well, danger moves are at least listed, and location moves don't seem to be mentioned again after that one line. If they are, I can't find it, and I'm kinda curious why I didn't get confused when I first read this too.
The hemming and hawing should not happen, you're right.
The problem here isn't on the player side. The GM is cheating. Accidentally, but still cheating.
GM Cheating in Dungeon World
The GM cheats in Dungeon World when they speak without following their Agenda, Principles, and Moves.
There is no GM move called "make an arbitrary decision." There's also no GM move called "have a freeform social interaction." If the GM is following the rules, this kind of stall should not happen.
This is why the GM has rules, to prevent situations like this one, among other situations that qualify as failure modes to avoid.
Responding to a polite request, as the GM
The player's job is done: they've had their PC ask politely. There is no error on the player side of the equation and nothing to fix, no other moves to try to bend to fit the goal.
Since the “everyone looks to you to find out what happens” trigger matches, it's now the GM’s turn to make an appropriate move, instead of falling into “time for unstructured social exchange improvisation!” habits that they have brought with them from some other game.
(Recall too that moves aren't optional when triggered: when that trigger happens, a move must be made; this is equally true for GM moves as for player moves. The GM's turns has been triggered and making a GM move is now demanded by the rules.)
There are several moves that the GM could make. All of them, if executed with the Agenda and Principles in mind, should immediately add something new and interesting for the players to engage with, not just chit-chat.
The trick is to pick one, and then do a quick mental Mad Libs to fill in the blanks that the move demands. Let's assume the PC has politely asked for that magic sword:
Reveal an unwelcome truth:
“Sure, you can have my sword! It's cursed. If you can take it from me, I'd be more than happy.”
Show signs of an approaching threat:
“What kind of a person asks for a warrior's sword?” the bandit chief growls. She's obviously really insulted just by the question. It looks like she's thinking of giving it to you, point first, if you can't mend the situation. What do you do?
or
“This old thing? Uh, sure! Here!” he says breathlessly. He almost pushes it into your hands, and then runs off. It's a very fine sword, clearly magical and worth a lot. As you look up from admiring it, you notice a posse of civilians with torches and pitchforks lead by three members of the city watch running in your direction. They're shouting something that sounds awfully like “Thief!” What do you do?
Turn their move back on them
Possibly the simplest and most straightforward move to make: ask them to tell you why in the world their polite request makes any sense! If they're asking in the first place, they might see a good reason that you're not seeing.
— Hm, you're just asking? Okay, well why do you think they would just give it to you?
— Because the village owes us their lives and souls, and we're heroes. He'll probably gift it to us.
— Huh! Well at any other time I'd laugh and so would he, but yeah, considering what you just did? Yeah, they gift you the sword. They even make a big ceremony of it. You're big damn heroes!
Give an opportunity that fits a class’ abilities
Have you got a thief in the party? Well...
He laughs that off. “Just give you my sword?! You must be soft in the head.” He turns and walks off, shaking his head and laughing. But you get a good look at his sword belt from behind and notice it's worn... given the right chance, you could probably cut it quick. Want to tail him?
Tell them the requirements or consequences and ask
This is a staple of responses to polite requests. This prompts the GM to set a price, and ask.
She says sure, she'll give you the sword. But only if you defeat her in single combat. She seems pretty confident too. What do you do?
or
“Sure. What's it worth to you? How about... that emerald necklace and arranging an audience with the Unmasked Lord for me? No? Well... let me know if you reconsider.”
or
“Hm, alright. Do you have three hundred crowns?”
or
“I tire of the burden. It is yours if you want it. But beware: the sword has a way of making heroes out of its bearers, whether they mean to be or not. Take it only if you are willing to shoulder that burden.” He holds the sword out, hilt first. What do you do?
The point is that the PC “just” asking is just the beginning, and there is nothing that says “just asking” is suddenly set in stone as the price at stake. The GM's job is to play to find out what happens, and to do that you pick a GM move, fill out its details, and play out that response. The result will almost certainly establish that there is a price beyond politely asking, either of in-game goods to exchange or in narrative branches the players must tackle. Rather than deciding, you add something interesting to the situation and then see what the players do.
So clean up the GM's side of these meandering social improv interludes, and you won't see stalls anymore! The GM might even be surprised by the things they spontaneously add to the game, faced with such circumstances. This is where Dungeon World shines: turning mundane, boring bits of play into pivotal moments, because the rules demand never doing something boring and stale.
Best Answer
Old Man Henderson is a problem not of game system but of game philosophy; Dungeon World tries to pre-empt that philosophy.
Some people will say "it was actually Trail of Cthulhu" but I think that's part of the status of Old Man Henderson as gaming urban legend that gets added onto. It was Call of Cthulhu, because you don't get to test to avoid SAN loss in Trail of Cthulhu, and you can't survive 15 SAN loss - Gumshoe likes to work in small numbers, SAN is intended to portray long-term degradation (short-term shock works on the STAB or Stability track), you're a goner at 0 and nobody can start with more than 10 or possibly 12. Call of Cthulhu's SAN works on the 0-to-100 scale.
I mean, maybe it's a game of Trail of Cthulhu that the Keeper was playing like Call of Cthulhu? That happens; people will try to play Dungeon World like D&D, too - just because the rules forward a particular philosophy, people can still break them to play as they please.
There are three pillars of philosophy that hold up the idea of Old Man Henderson: the GM's plot as precious thing, the GM as neutral arbiter of an adversarial situation, and the secret player power.
The GM's Precious Plot - "DO NOT pre-plan a storyline, and I'm not fu[nn]ing around"
Most Apocalypse World derivatives will take the swears out of that, as I've had to, but the idea remains constant. It doesn't mean "don't prep" - you absolutely should prep, but what you should prep are groups and places and philosophies. You shouldn't prep "a line" - the bright thread of prophecy that when severed plunges the world into darkness, or a single narrow path of actions you have no idea how to act outside.
Here's a scenario in Dungeon World where some PCs do the Henderson thing, destroying what would might be viewed as the first vital step in a story of (perhaps) a king who craves the power of antiquity but will call up things he cannot put down. But their violence was only against the king's agents; the king still craves. Old Man Henderson, an agent of unreasoning violence and destruction, can only shut down a front by annihilating it utterly -- and if it actually comes to that point, the GM has got all the mileage they need out of that front anyway.
Judging a Rigged Game - "Play the game with the players, not against them."
The philosophy can be summed up, perhaps unfairly, as "prepare adversarially, run neutrally". Prepare a threatening place full of threatening things, but when it comes time to game, put the idea of threat aside and run fairly according to the rules and your own precedent. In the worst case, this can often lead to an odd sense of pride as a GM; pride that you built opposition that could take the PCs in a "fair fight". Old Man Henderson comes into this and either plays by rules that disproportionately advantage the PCs, or takes improvised actions that the GM has to adjudicate in the moment and are fair game for PCs to argue over their relative fairness.
Apocalypse World and its derivatives tend to point away from the dispassionate style of playing. Name everyone, give everyone life, but also be a fan of the players' characters - neither of them are dispassionate things to do. Nothing limits what the MC can do when the game's on - "make as hard and direct a move as you like" is a common refrain - but the MC also doesn't get to be protected by a principle of impartiality, and is accountable for their taste to their players. Everything the MC does to you is because they want to.
Old Man Henderson can take refuge in audacity, because the GM is trying to be the disaffected reasonable judge and is thus obligated to take him seriously. A Dungeon World GM is a participant in the conversation and doesn't have to play down their own desires.
The Player-Agnostic GM - "Offer an opportunity that suits a class's abilities"
Another element of the Old Man Henderson mythos is his 300-page backstory, written partly in Enochian, lost tongue of the angels (or something like that). Apparently it justified everything he had access to, even though the things you have access to are kind of controlled by the character creation process, and you can't ignore build points with a 300-page backstory, any more than you can ignore hit points because on page 250 it says you submerged fully in the river Styx and are invulnerable.
But the idea here is something I've seen elsewhere - that the GM should leave the players to manage their own character sheets and shouldn't concern themselves with what's on there. I can kind of see the wisdom of this, especially for novice GMs in a system with complex and volatile player powers, like a cleric's daily spell loadout in 5E D&D.
However, it really falls apart in the face of the demands of Apocalypse World and its derivatives. If you don't know what moves a player has access to, through the combination of basic moves and their playbook, how can you possibly judge whether they've made a move or not? How can you be a fan of them and offer them opportunities without knowing what they're capable of? How can you activate their stuff's downside if you don't know what their stuff is or what its downside is? (Seriously, if you're running Dungeon World, even as a one-shot, have a second copy of the playbooks that you can keep for yourself as GM reference. You'll thank me, unless maybe your play surface is baby-sized.)
Nevertheless, Henderson can persist.
Old Man Henderson was born out of a desire to ruin whatever the GM was planning. That desire can still exist in players, out of spite over past transgressions or just because it's how they choose to approach the game. It doesn't matter the system that it's in.
But in an Apocalypse World system there's less to hide behind, if nothing else because the GM is supposed to be a fan of the players, needs to know what they want out of the game, and has the power during play to give it to them. Eventually it's going to come out what the Old Man Henderson player wants to do, and everybody can confront it there.