I think this all came down to matchups and personnel and Carroll has said as much in his post game press conferences. He said that he wanted to use the clock and throw on 2nd down, and then use 3rd and 4th down to run it need be. However, the mistake he made and publically stated was that the Pats were in their goal line defense, which is why he thought the passing play would work. Obviously, the Pats weren't in the goal line, because Butler wouldn't have been on the field if they were. Carroll misread the personnel on the field, and in addition, he didn't have his goal line offense out there. Had Carroll trotted out the big dog/goal line offense, you might have seen BB use a timeout immediately before the snap, but as it turned out, BB got exactly what he wanted. He had the right defense on the field against the offense he wanted (a shotgun snap from the one yard line).
Don't get me wrong, I almost lost my voice screaming at the television for BB to call a timeout, but in retrospect, he outmaneuvered Carroll like only the best coach in the history of the game could do at that moment. The fact that he had his defense, and a no-name defensive back, practiced, ready and waiting for that EXACT play was just icing on the cake. Butler and Browner then executing it perfectly. Well, it don't get no better than that. Football is a game of chess, and Carroll got beat by the greatest grand master of all time.