The Obvious Answer
The pat answer is that the player is clearly signalling that they aren't interested in simulating time spent in town with any degree of granularity. They want to show up, hit sell, and get on with the adventure.
The sense of time compression may be a result of their minimizing the importance of the tasks. It could be because they feel "penalized" when they're told that a task takes too long. Or it could be that they're concerned that they'll be caught in mid-task if it takes too long.
In any event, it seems clear that the player isn't that interested in sitting around in town for too long. Is this something that you can compromise on?
A More Useful Answer
All right, so we all hate the obvious answer.
In my games I've always worked the abstraction. I go around the table, and each player tells me everything they want to do at a high level (i.e. "sell my stuff, and look for magic armor +8"). I tell them how long it will take (and what rolls are necessary), and give them an opportunity to modify their request. Then move on to the next person.
Once you get an idea of what everyone's doing, sprinkle in role playing scenes and random encounters in montage fashion. Just avoid springing anything that's likely to interrupt the overall process.
This is essentially the same concept as crafting. You wouldn't let a player give you the blow-by-blow of their crafting session to save a little time. The same applies here.
Increasing abstraction does, necessarily, decrease the opportunity for role playing. It doesn't eliminate it in this case, but it is something to be aware of.
Introductions
The real problem you're going to have is changing how you've been doing things. Players are going to have a hard time going from doing something in a day to doing something in a week, even if there's no mechanical difference.
Step one is to communicate with the players.
After that, give them useful choices when it comes time to make their rolls. If they want to sell something faster, give them a range of options (you get full book value if you wait several months; half if you sell in a nominal timeframe; quarter if it must go now).
If a roll is required, give them the option of increasing the difficulty to accomplish the task in less time (i.e. base time one week, subtract one day for every five added to the difficulty). Failure means a reroll, resulting in things taking longer.
And bribery never hurts... If nothing else, giving them something they couldn't otherwise get through taking extra time (a bit higher sell value, a cheaper price, and so on) can help swing things in your favor.
Some More Thoughts
Sleeping on this, it occurred to me that human beings actually act like this all the time. We strive very hard not to be idle during our daily lives.
The big difference is that we favor low-activity tasks that give us biological incentives: We savor our meals, engage in idle conversation, read books, watch TV, sleep late, etc.
The gap you're seeing between "realistic" behavior and what the PCs are doing is because they've stripped out all of this idle activity. Why? Because they're not receiving the real-world incentive for this sort of thing (dopamine, endorphins, etc.) and these activities are extremely boring to roleplay.
The Urban Campaign
One of the key assumptions of most of the above is that in town means downtime. Encounters continue, but the assumption is that these encounters will usually be more socially oriented, less threatening overall, and unlikely to disrupt the ongoing processes of town life.
This lets players fudge their sheets a bit. It doesn't matter whether you have that new sword yet or not, you can still take part in what's going on without holding anyone back.
Campaigns with a heavy urban component violate all of these assumptions. Players need to be in top form at all times, because a top-tier encounter could happen, or a thread could pull them out of town on short notice.
In this case, waiting a week for an item to be found gives the players an awkward choice:
Be actively looking for the item for a full week. Sit idle while the rest of the group enjoys a week's worth of adventuring.
Endure pointless red tape. You've picked the item you want, you've probably paid the money, you've made the roll, but you can't update your sheet until the GM nods at you some arbitrary point in time later.
Get the item right away, but "say" you're taking a week to get it. Wha..?
In any case, that's a lot of annoyance for a pretty small gain in verisimilitude (or a really weird drop in verisimilitude for no perceived value).
Urban Solutions
While it's harder to do, there are still a few things you can try to mitigate these tendencies.
Employ Gating
Give the players a buy limit. They're free to buy whatever they want, as long as its value is below X. This will tend to lead to periodic frenzies of buying, making it easier for you to lock down the game world, and decrease the problems listed above.
Whenever you increase the buying threshold, treat that as downtime, and abstract it as described above. Minimize active top-tier adventuring, and let the players go nuts.
The goal is to get everyone buying at the same time (so hopefully the players aren't poking the game world), and to have the game world stop poking them back long enough for them to get their items.
Skinned Gating
I'm still having trouble groking your full situation and requirements, but for the sake of posterity here's some notes on skinning a gating system. I don't think this will necessarily work for you; it requires periodic lulls where the game-world isn't actively trying to get the PCs attention. You can come up with individual reasons, but there's no really good general-purpose reason for this (although it's worth noting: If your game world is constantly poking at the PCs, that may be part of the issue).
Step One: Establish the gates
The first step is to divide the items in the game into different gates. Most DMs use gold-piece value (i.e. a buy limit) because a. all buyable items have one, and b. it's roughly equivalent to how powerful the item is.
That said, you have other options. Some systems support legality and availability codes for individual items (Shadowrun and D6 Star Wars come to mind). You can, naturally, come up with ratings of your own.
Step Two: Apply the gates to your players
Most DMs simply leave the gating itself up to the players. "You can buy anything up X gold-pieces;" "You can buy anything up to availability 3." This has the advantage of decreasing the amount of player/DM bandwidth (a very limited commodity), but can feel kind of gamey.
You can soften this up a bit by keeping availability somewhat secret ("That's a highly regulated item"), and having the players ask for it.
You can also use "soft" gates to make things feel a bit more organic. An at-gate item might be a nominal difficulty, a significantly below-gate item an easy check, and an above-gate item extremely hard.
The down side to these techniques, of course, is that they occupy table time. The upside is that they make things feel a bit more organic and mysterious.
Step Three: Advancing Gates
There are several different techniques you can use to explain a gate advancement. Here are a few examples. I'll tend to use numbers in the explanation, but you can of course use in-world explanations.
Location, location, location.
In our little town, you can only get availability 3 items. Make the trip to the capital and you can get up to availability 6. Find a safe route to the lost city of the dwarves, and you can get availability 12 items!
This is particularly effective if the goal is to move the players around over the course of the campaign.
New blood in town
As the story progresses, the players' influence may result in the city becoming more favorable to merchants (either legitimate or not-so-much). Or perhaps the city is simply growing over time (depending on your setting). Either way, an influx of new merchants or the establishment of new trade routes could be used to explain a higher gate-level.
Powerful allies
NPC wizards, craftsmen, nobles, or merchants helped or extorted by the PCs could all be used as an explanation for a higher gate level. Either through crafting the items directly, allowing access to vaults, or by using their connections to import the desired items.
Licenses
If you use legality as a factor in item availability, you can turn the acquisition of licenses or special dispensations into quest hooks of their own.
Change your magic paradigm
In your description above, it sounds like you're leaning towards the "magic items are special and unique" school of play, while your players are leaning towards the "magic items are an integral part of the character" school of play.
You could always try yanking the dial all the way over to the "magic items are special and unique" school, and eliminate the ambiguity. Players don't shop for magic items... They encounter them in quests and adventures.
If you go this route, be sure to give the optimizers something to replace the magic items they used to find easily (so they don't feel less powerful as a result). Something along the lines of the "inate bonuses" concept in D&Doid games.
As usual, communicate, let the players know that things are changing, etc.
When I as a DM have an opportunity to make a major change to a character, such as character death, conversion to a villain or non-villainous NPC, etc, I will bring up the issue with the player. It means you can't surprise them, but by asking their opinion and inviting their input on the idea, you can not only find out whether they will accept/enjoy the change, but also get additional ideas for ways to improve the change.
A few examples: A player was playing twins, one of whom was rather... homicidal. I realized that one of my NPCs would very much want that twin on his team. So I spoke to the player privately between sessions, to see how he would feel and how his character might react to a proposition from the NPC. He was thrilled by the idea, offering several suggestions for how his character could work as a villain from within the party for a time before converting completely. His character ended up becoming a miniboss for heroic tier.
Another player ended up being the Bearer of the Holy MacGuffin for the plot - the character responsible for carrying the items that the villains wanted. I warned him (both in and out of game) that this made him a target for the villains, and that they would focus their attention on killing him. His response was "bring it on!"
By talking to your player out of game about your plans, with as much or as little detail as you're comfortable with, you can gauge their reaction to your idea. If they're totally, completely opposed, you should probably change your plans, since your goal as a DM is to ensure the game is fun for all your players. However, my experience has been that, given enough information to feel that they're "in on it", players will generally treat such plans as a challenge to overcome or as a story component to expand upon and play with.
Players like to have choices, and like to feel that they can influence the plot and change their own destiny. Offer them this opportunity, and they will rarely be upset.
Best Answer
I think a lot of the answers in How do you help players not focus on the rules? are on point here as well. They talk about limiting time spent discussing and taking things offline, but perhaps the most important is establishing that your rulings stand and that as a more experienced player, and additionally as the GM, your interpretations of the rules are the ones that take primacy. Even above the books, if it comes to that, but certainly in absence of clarity or obvious error.
You can allow a bounded amount of "look it up time" if you want, but I don't really have the patience for that personally. "You can look it up when we're not in the middle of doing something and prove me wrong later if you'd like, but now's not the time" is a valid GM ruling. This process could be made faster by having the SRD up on a computer, having him perhaps print out his spells he's using for quick reference, etc.
How to handle a rules-lawyer player? is also relevant - though the context there is someone who DOES know the rules being argumentative, most of the answers apply to someone who doesn't as well. One would hope that being wrong all the time would slow your particular rules-lawyer's roll, but it sounds like it's not for whatever reason.