I see what you mean about the short passes and run game. However, I don't think that has anything to do with trust in QF's passing ability. I think a lot of people forget that CWT wants to run the ball. I don't think CWT has ever stated anything different, in fact he has always said he wants a power running team. When Mack averages 7 ypc, why would you try to over complicate it.
This scheme of running 70% of the time and quick, short throws, forces teams to stack the box. Which leads to all the big plays off of play action. I have heard the arguments that if they respected QF's arm it would open the run game up even more. Yes, however, the offense is designed to bring the defense in, then go over their head.
I don't think QF is instructed to go throw his progressions. CWT has even stated that he instructs him to go through the 1st read and if that's not there, look to run. I think as the season went on, you saw QF do less of that, and look for the pass play. Im sure you seen it where instead of taking off he would just scramble to keep to play alive and keep his eyes looking for a receiver. I honestly thought that was QF's biggest strength, that he knew when to pass it, and when to just take off and get the yards.
He does become inaccurate on the move though I agree. Also, I agree that if he gets moderately better in the passing game, we could be looking at 10 wins. Like everyone has pointed out before, there were times when he would just go completely cold and become wildly inaccurate.
In saying that though, even if QF becomes a great passer, I don't see CWT going away from the running game. Ever. It's just the offense he wants to run. It's just like Mike Leach will not go away from the pass, even when it is not working. CWT will stick with the run game, even if it is getting stuffed.