Go look at any of those teams, and they all passed more efficiently than their opponents in the playoffs. If Dilfer hadn't been efficient in the playoffs, and if their defense hadn't stopped the opponent from passing efficiently, the Ravens wouldn't have won it all. Running and stopping the run means very little, except for the effect it might have on passing. But it's by far more important to pass the ball better than your opponent than it is to run it better. Even if you base your offense around the run, you still have to be efficient when you throw it (Dilfer was), and you have to stop your opponent from passing efficiently (the Ravens did).
Not even close. In the NFL, it almost never matters if you run the ball better than your opponent. If you don't pass the ball better, you will almost always lose. There is all kinds of research that shows this to be true.
Like this, for example --
http://www.twominutewarning.com/correlations2.htm
The correlation between passing effectiveness and winning is twice as high as that of running effectiveness, and it's more than twice as high for yards per pass as it is for yards per rush.
Or, look at last night's game as the perfect example. Which team ran the ball almost at will? Which team could barely run it at all? Which team passed almost at will? Which team kept throwing interceptions? And which team won?