I don't think anyone has said, "Running doesn't correlate to winning.". The argument is "Correlation doesn't equal causation."
No, the phase that running or rushing does not correlate to winning was repeated ad nauseam. It was a constant topic a few years ago.
What that crowd completely failed to consider was the relationship of rushing and passing.
Defenses will adjust to limit rushing or in the Cowboys case they'll to adjust...
That means that a defense can face two offenses and hold both the same number of rushing yards but in one game they play 8 men in the box on all snaps and in the other game they never play 8 in the box.
- The offense that forces the defense to play 8 in the box had an advantage in the passing game.
If someone were only looking at rushing yards, then they would never distinguish between those two situations.
Both this season and last many of the Cowboys fails in pass defense have been directly attributable to having to move players up in an attempt to stop the run while weakening the pass defense.
This season when they've tried to play Nolan's preferred 2-deep Safety coverages, they've often been in a situation similar to LBs in play action where a Safety would start cheating up against the run and then the offense would go deep leaving CBs with no help.
Last season they often played the SS up within 1 yard of the line but he still have coverage responsibilities. They managed with Heath doing that because he had the speed to get back in coverage but when he was out for multiple games it got really ugly because his replacement didn't have the speed to play that style and had to play 5 or more yards deeper than Heath played which just made the run defense worse.
The Cleveland Browns are 5-2 this season coming into this week because they've been a brick wall in run defense.