The Patriots run the ball, but it is out of an almost spread offense. Brady throws the ball loads. Granted, they do play great defense, but they don't win by running the ball.
The establish the intermediate pass, loosen up the defense, then run.
I named them as the exception so I don't know what your point is.
Again, look at the QBs in the playoffs: Brady, Roethlisberger, Cassel, Manning, Flacco, Sanchez, Ryan, Cutler, Vick, Bradford, Brees, Rodgers. Now look at who they've got running the ball: Green-Ellis, Mendenhall, Charles, Addai, Rice, Green/Tomlinson, Turner, Forte, McCoy, Jackson, Thomas, Brandon Jackson. Yeah, you need to be able to run the ball but most of these teams don't have an elite runner, but they almost all have top QBs. In fact, if you flipped Schaub and Rivers for Flacco and Sanchez I'd say those are the top 12 QBs in the league. Can't say the same about those RBs.
You are just looking at name value alone and not production. I didn't say you need an elite runner but rather a run game. If you want to name your top 5 or so QBs in the league (without any order) it would look something like this:
Brady: The exception
Manning: Battling for a playoff spot despite his greatness
Brees: Just clinched playoff spot through spotty performance whole season but finally run game and run stopping showed up
Rivers: Missed playoffs despite being MVP candidate
Rodgers: Also battling for a playoff spot
Vick: Clinched division
1/3 of the top QBs in this league, legit elite QBs in this league, have clinched a playoff spot.
You can run through all the others and the common theme is they run the ball effectively and they stop the run. If they can't do that you've seen what happens.