Our win isn't "demonstrably better" in the eyes of the committee- they view Michigan state and Kansas state almost equally. TCU had some near misses, but we did too (remember the double OT game against a penn state team that will finish 6-6? Or losing in the third quarter against Indiana?)
The Big XII has some bad teams but it's still better than the average big ten team. TCUs SOS is in the 30s while ours is in the 50s. I'm not sure why you're trying to write down their Baylor loss. Even if you think they're terribly overrated, they're world's better than Virginia Tech by every measure.
All that said, I think if our resume was: wins over MSU, Wisconsin, Minnesota, bad loss; that trumps wins over Kansas state, Minnesota, respectable loss.