Yeah look at Indiana in the 3rd video. Somewhere around the 1:50 mark. They ran 3 consecutive plays from the shotgun and AS SOON AS THE BALL IS SNAPPED, there are 3 or 4 guys in the backfield. I know it is Indiana, but come on...
2:37 of video 3, he does not hesitate at all! and also, to go with what you said, QB's also have no idea when to hold on to the ball and when to hand it off.