First, that isn't true. There are many, many other statistics with higher win correlations.
Second, you're confusing cause with effect. Teams that are winning run a lot in the 4th quarter, so you get correlation without causation. If more running really led to wins, all 32 teams would simply run more.
I haven't seen a stat that you provided that is better than 80%. I know you've posted some things before and forgive me for not wanting to search for them. Could you please give me your top ones again?
And you are right about causation. That's the thing about football, its all intertwined. Teams do try to run. The really good teams do it well enough that they can continue to run the ball throughout the game. And yes, teams do run the ball more when they are winning. It helps drain the clock. But even that is situational. Just because you are up 3 points doesn't mean you just now automatically run the ball.
Running more or passing more is something that can be controlled.
If you can run efficiently through the course of a game, then it is less risky than passing. That is the objective. But if a team runs 10 plays in a row and does so efficiently, then the defense will undoubtedly adjust. Most, if not all, defenses can shut down an aspect of the game. If they put all 11 guys at the line of scrimmage, they will stop the run. But doing that opens up the passing game.
It really is about balance. Run enough and efficiently enough to put the offense in favorable match ups when they do pass. Thereby reducing the risk of passing.
Troy Aikman and the early 90s Cowboys are the perfect example of this. Our own Cowboys of last year are a perfect example of this.
Aikman never really put up huge numbers passing. He could have, but why? They used the running game to break teams down, then used the passing game to keep them honest.