Well, I think a lot of indie games-especially, several of the narrativist "story" games are built for
a. players that don't trust the GM
b. players that like to DM, but don't want to give up that control as a player.
Hmm. Having played and enjoyed a number of these games, I don't think this is quite fair. They really are trying to do something very different than a game like D&D.
In a narrativist game, one of the key ideas is narrative control. The players need to be able to shape the story, or dare I say, the narrative. The rules define who, at any given moment, is doing the shaping. The GM often is that person, but by no means always. (And I might add that not all narrativist games even HAVE a GM. It takes some tricky design, but it can be done.)
A D&D-like GM would defeat the whole point of a narrativist game. It really has very little to do with trust, and everything to do with what the game is trying to accomplish.
I love playing D&D and games like it, but they scratch a very different sort of itch than narrative games like Prime Time Adventures or Capes or Universalis.
In PTA, you're almost more like a creative team writing a TV series together than anything else. (The GM is actually called 'the Producer'.) You do each have your own character, and you do play them in-character at times... but in between it's both appropriate and expected for other players to suggest ideas about where the plot is going, what the scene setting and background music is like, even how your character should deliver his lines.
I once had my character give an ominous speech, and another player said, "Oooh! No, wait, he should say it THIS way!" And I said, "Wow! That's even better!" and did the speech over again. (I should add that I didn't have to. But in PTA, it was totally acceptable for her to suggest it, and for me to take the suggestion.)
It sounds crazy from the perspective of playing D&D, I know. These really are an entirely different class of games, in which the GM plays an entirely different role. I find them deeply enjoyable, but as I said, in a completely different way than how I enjoy D&D.