Compels are used to increase the amount of story occurring, using a form of reincorporation of a player-chosen theme (i.e., an Aspect). This is often negative because we tend to tell stories where the rising action is composed of challenge and setback, but compels are not necessarily negative suggestions. Their purpose is to complicate or add nuance to the situation or to advance the action in a surprising direction. They can just as easily be positive or neutral from the character's point of view.
A space marine with the Aspect "A lover in every port", while trying to seduce someone, might be offered the obvious negative compel that a jilted lover shows up and causes drama. Equally, if that marine's trying to find contacts who can repair a beam rifle that's illegal to own locally, she might be offered a positive compel that she has a former lover on the station who brokers black-market services. Either way, if the player accepts the compel, the story has taken an interesting turn that the player is automatically invested in because it's tailor-made for their PC. That is the power of the compel, and it transcends simple negative challenges.
Of course, as referee I could just say the helpful contact is there. By offering a compel, I'm putting it in the player's hands to decide, and feeding the Fate point economy. Likely they'll take it, so the net effect is the same but I've added another Fate point to the economy. I don't mind being generous with opportunities for giving Fate points, and by being so I also fund their ability to turn down "positive" compels, increasing their story control (and therefore, investment). Do it enough, and the few times that they want to turn down the positive compel (and so have to pay for it) are more than made up for by the extra "free" Fate points they've been getting, taking care of the potential for it feeling unfair when they reject it. As a general rule in Fate, anything that increases the number of Fate points moving around (not just being given to the players, but also given and spent) is likely a good thing for the game.
One thing I like about the text of Diaspora is that it belabours the ways in which Fate can put the power into the players' hands (and, not-so-sneakily, take some load off the referee). One of the specific ways it does this is to point out that players can ask for compels. Hence, even a negative compel, when asked for, can be a positive thing as far as the player is concerned.
First off, DFRPG is full of "the group should agree" (YS92), "keep in mind the intended play style" (YS31), "make sure your players are okay this" (YS338), "make sure you're on the same page as your players" (341), and "when in doubt, talk it through with your group" (YS99).
In many places throughout this book, the phrase “the GM decides” is often used interchangeably with “the group decides” regarding some of these issues, because it emphatically isn’t the GM’s job to run a dictatorship—every player should always be allowed the chance to have a say in those instances. The GM should act as more of a moderator, synthesizing the group’s input with her own in order to reach a final decision. [YS306]
But I'm going to focus on the Lawbreaker thing, because that's a lot more quotable, rather than an obvious system philosophy.
Concessions
A concession has to pass muster with the group before it is accepted [YS 206]
This is framed in the context of a concession not being too lenient; it must "represent a clear and decisive disadvantage for your character." However, I see no reason that an extra-harsh concession (like death) should be able to bypass the group approval requirement.
Lawbreaker
The section on the Laws of Magic discusses them in terms of choice:
Whenever you choose to break one of the Laws of Magic, you’re crossing a very real line. [YS232]
Once a character has chosen to cross the line and break a Law of Magic, that decision is a part of him however you look at it. [YS233]
But then the section on the First Law says,
This is one of the easiest laws to break by accident [....] Accidental deaths can happen, and in those cases killing with magic still counts as killing when it comes to the Lawbreaker stunt. [YS235]
This seems to be an invitation to the GM to orchestrate accidents, but it's not: it's a statement of in-world assumptions, not the game's philosophy. I can say this with certainty because the very same section immediately says,
Your group should discuss how important they want the First Law to be in play. [YS236]
Ultimately, the GM needs to be careful and conscious about putting life-and-death human adversaries in front of the players. [YS236]
And makes very clear that this isn't about creating a bunch of outlaws, but about
[...] giving the First Law a strong and palpable presence in the game. A number of players might enjoy this as well, welcoming compels directed at, say, their Wizard of the White Council aspects to remind them that the First Law is an obstacle to their actions when a life is on the line. [YS236]
So that seems pretty clear: both concessions and the breaking of laws are in the hands of the group as a whole rather than the GM exclusively, and interesting narrative is at the fore of the game philosophy. To make it absolutely beyond doubt, I'll finish with this:
Who determines that a character has crossed the line? This is something that a gaming group should decide on as a policy for their specific game. [YS234]
Best Answer
There's a huge Chekov's elephant gun you need to be aware of when playing a mystery game: The mystery is there to be solved! There's nothing interesting about not solving the mystery.
So since the players are going to solve the mystery anyway, the big question in the game shouldn't be about -if they can-. They can and will. It should be about -how they do- and -what it costs-. The former is your players' domain. The latter is (as the GM) yours.
Fate insists on sharing information with the players in the form of aspects. Players need to know about the aspects in the game, including aspects about your mystery, to be able to play as intended. So hiding away those aspects kills a Fate game quite quickly.
So you need to lay your mystery open on the table. And let your players tell you how they solved it.
Meanwhile, you should ask them a lot of questions about how they solved the mystery. And act on their answers. Challenge them, let them bleed on the way. Take your toll.
Put up obstacles and opposition they must defeat to get to the result, and make them roll. But never let failure stop them. Make failure cost them.
Mess with their characters as much as you can. Being "taken out" in Fate does not necessarily mean that the character is out of the game. It means that the player temporarily loses their control over the character. When you take them out, grab their sheet and rewrite one of their aspects. Swap some skills. Tie what you just did into the story.
One of the outcomes in Fate is "success at a cost". Offer them devil's deals whenever they roll poorly. Tell them that they can still make that interrogation subject sing like a mockingbird, but it is going to cost them their "badge of honor" aspect.
The mystery will eventually be solved, but the characters that solved it won't be the exact same characters the players began with. They will have changed along the way and the story will be about that change.