I think the statistics show that having a good running game increases your chances of success.
For example..
KSU - Auburn - KSU had 27 yards rushing, 289 passing. (Loss by 10)
KSU - San Jose St. KSU had 152 yards rushing, 272 passing. (win by 20)
KSU - Missouri St. KSU had 221 yards rushing, 325 passing. (win by 49)
KSU - Texas - KSU had 113 yards rushing, 217 passing. (win by 20)
KSU - ku - KSU had 53 yards rushing, 310 passing. (loss by 6)
KSU - CU - KSU had 249 yards rushing, 214 passing. (win by 27)
KSU - OSU - KSU had 125 yards rushing, 404 passing. (loss by 1)
KSU - BU - KSU had 208 yards rushing, 255 passing. (win by 38)
KSU - ISU - KSU had 78 yards rushing, 347 passing. (loss by 11).
Just looking at those numbers, and only for KSU, when the numbers are more even, the balance is there, KSU's success is much more definitive in terms of scoring.
I'd say that maybe the red-zone correlation isn't as significant as is the ability to run the ball and control the game. Doing so, means you can end up winning the game.
So when Prince says we need a running game to help win games, I think it shows pretty well that having one helps us win.
Perhaps, that's the better relationship.