Anyway, here it is:
I always thought that the "miniatures take away from the roleplaying" argument was a bit of a cop out. I've never noticed any link between having figures on the table and people's willingness to roleplay.
As far as an issue of trust, it's more an issue of power. Trust is only a byproduct of an inequity of power. If someone doesn't have power over you, you don't have to worry about trusting them. There isn't anything they can do to you, so why worry about them?
So, what does this have to do with D&D? A lot.
In D&D, the DM has more power over the flow and implementation of play than the players. However, the players have the rules to keep the DM in line. So, if the DM throws Tiamat at a 1st level party, the players can call out the DM for throwing a CR 20+ monster at them. After all, the rules explicitly say that's wrong.
More importantly, the players can use the rules to stake control over different aspects of the game. One of the aspects of D&D that makes it so interesting is finding advantages and combinations that are more powerful than the sum of their parts. When a player puts together a character, he's constructing a spread of talents that he hopes proves fun to play.
We can define fun in a lot of ways, but I think for most D&D players fun is "having a positive, noticeable impact on the flow of play." This usually means a PC who kicks a lot of butt in whatever area he chooses to focus on, be it roleplay or combat.
Without miniatures, you short circuit a lot of the possibilities for combat-focused mastery for a player. You turn a lot of abilities and spells into "mother may I"* abilities - the DM decides when a player can use the feat, not the rules. That's a subtle but important difference. The player's feats only come into play if the DM wants them to. The player's choices are less important, because the DM can now arbitrarily put them into play or yank them out. That's the basis of the power divide between players and DMs, right there.
So why is there a natural tendency to link miniatures with games that feature no roleplaying? I think there's two factors at work. For players, combat is one part of the game. If you aren't very good at tactics, pushing those miniatures around a grid takes away from the parts of the game that you do like. I think that it's human nature to prefer to say "Miniatures take away from roleplaying, let's not use them" rather than "I'm not good at tactical combat, let's not use minis."
For DMs, things are a bit different. IME, there's a natural tendency for DMs to houserule the game to weaken the game's leveling effect WRT DM and player power. That's a post for a completely different thread, but it's one of those things that you really have to watch out for as a designer. I think this tendency is an artifact of 1st and 2nd edition, and I'm very curious to see what the culture of the game is like in 10 years.
So, in the end the question isn't "Do you trust the DM?" The question is, "Why doesn't the the DM trust the players?" If we're taking power away from the players and giving it to the DM, why are we doing this? What purpose does it serve?
Now, the two cases I outlined above don't apply to everyone, but they are the most common ones IME. In any case, I hope it provides some theoretical framework for why miniatures are a part of D&D. I think that D&D 3e is so popular precisely because it is the one commercial game that seeks to bridge the power gap between the DM and the players.**
*A "mother may I" ability in D&D is a PC talent that works only if the DM allows it to. The ranger's favored enemy is the best example - the ranger can only use it if the DM puts monsters into the adventure that qualify as the ranger's favored enemy. IMNSHO, mother may I abilities are bad for the game. Turning undead is an exception, since you can take feats to do different stuff with it. Generally, these abilities are bad because they exacerbate the power divide between players and DMs.
**Oddly enough, a lot of indie RPGs' defining trait is their move to level the power difference between players and DMs. In many ways, indie games have more in common with D&D than any other game on the market. Just don't tell that to the people writing indie games... =)