While I don't completely disagree with you about "trusting his arm", I think it has more to do with him being coached to not turn the ball over. If you look at his decisions throughout the game, he tends to make the "safe" throw early in games. But when it gets to the 4th Quarter, and he needs to make plays to either mount a comeback, or sustain a big drive, he tends to force the ball more and make throws he doesn't in other times of the game.
His passer rating in the 4th quarter is noticeably better than in other times. So, again, given Fisher's MO, and his emphasis on not turning the ball over, I would guess that its more than Bradford just not trusting his arm.