Again: allowing new mechanics, or not allowing them, can have nothing to do with trust in the players. Nothing. And I put the word in italics and everything, so you know I must be serious.
My watchword when dealing with player requests: is it fair? Is it fun?
An easy example: I love plenty of games with guns in them, but I detest gunpowder in D&D. I don't want to mix my D&D and my firearms because I don't like the feel. Such games aren't fun for me. If Sagiro, one of my best friends and a superb DM in his own right, asked to play a gunslinger I'd say no. It has nothing to do with trust or character balance—I trust him implicitly in all aspects of gaming and real life—but gunpowder doesn't doesn't fit in my world, so the answer is no.
Hussar, you keep conflating the two, implying that a DM using good sense is somehow betraying her players' right to unlimited choice. That right doesn't and (in my opinion) shouldn't exist.
Interestingly, in my above example, I might work with the player to reskin the gunslinger as a magical wand-wielder, assuming it was the mechanics and not the flavor they liked. I'd find that fun. But I reserve the right to reject rules based on mechanics as well, especially if those rules aren't fair to me or the other players. Designers in Renton don't know what works wonderfully in my game as well as my players and I do. I remember way back in 2nd edition when a player tried to talk me into letting his race be "polymorphed young silver dragon." That'd probably be fun, but it wouldn't have been fair to the other players. I declined, and he happily picked a human.
My take? If you don't like a DM's gaming style or campaign, it's fine if you choose not to play with them. Same thing for a DM choosing not to include a player who's a bad match. But a single player doesn't get to unilaterally force feed their wishes on the rest of the group. That's neither fair or fun.