According to Big 12 principles, the tiebreaker is head to head. It's pretty clear that the Big 12 commissioner refuses to recognize a "True Champion" because he wants both Baylor and TCU to each be viewed as conference champions with zero downside. It's bush league stuff, and it's completely unfair to the other Power 5 conferences.
If the committee views TCU as a true conference champion, then who's to say the SEC abandons their conference championship game in the future and labels ALL 14 teams as having a share of the SEC championship? If 1/2=1, then why wouldn't 1/14=1? For this reason, I believe that with a Baylor victory tonight that TCU should be viewed as a non-conference winner, and thus be on the outside looking in.