If we had a passing attack that legitimately threatened opposing defenses in anyway then our running game would have opened up easily and been a huge strength.
That's probably a bit tough on the passing game. They were 12th in the NFL this year based on passing offense.
That plus Brady means that our passing attack is always a threat to other offenses. I think at the end of the season though we realized that we could much better exploit this strength by getting a number of receivers on the field and forcing the other teams to come out in defensive-back packages. Cf. the San Diego game... we did struggle to run it but out of the spread running the draw was quite successful. But you don't want the draw to be the basis of your run game.
It doesn't seem to me that the passing game is a necessary condition for a good run game. For example, San Diego, Denver, KC all had worse passing offenses than ours but we know all about their running games. So I guess my assertions are:
(1) the passing game wasn't that bad
(2) a good passing game is neither a necessary nor sufficient condition for a good running game
(3) on that basis other factors are clearly important. I think they're well illustrated by the previous examples - talent helps, and blocking is crucial.
Let's not try and reduce this down to one area because to my mind, none are sufficiently explanatory. If we asked BB what he'd thought, I'm sure he'd say we have to do a better job with the blocking, with the running and with the play calling.
Edit: just an interesting addendum: Atlanta had the #1 rushing attack in the league, and the #32 passing attack.