I'm not so sure. Bama is also 12 - 1, a conference champ, and they just defeated the no. 1 team in America. True, Texas beat them, but I'm not sure that will signify.
I hate to say this. I despise Bama and all its works. But I'm not sure they won't squeeze in.
So regular season games don't matter? I remember the SEC pitching fits about expanding to a larger playoff system because it would dilute the regular season and EVERY regular season game should count. (Until they had TX and Oklahoma planning to join, then they wanted the expanded playoffs) Do regular season games count, or do they not count. Or maybe regular season games count when they benefit you, and they shouldn't count when they don't benefit you.
I would probably be OK with most sets of objective metrics that could compare teams. What I am not OK with is changing the metrics every year to match the desired result.
Going by what Bill Hancock has said in the past: There are three undefeated P5 programs. They are in a class by themselves based on win/loss and conference championships. There are four 1 loss P5 programs. Two of those have conference championships. Three of those have common games.
Ohio State -- no championship -- no common games
mutts - no championship -- Lost to Alabama -- Lost to common opponent that Texas beat
Alabama -- championship -- beat mutts -- lost to Texas
Texas -- championship -- beat Alabama -- Beat common opponent that mutts lost to
Ohio State has no claim to be in. Georgia has no championship, lost to one team, and lost the common opponent argument with Texas. Alabama and Texas have a championship and Texas won the head to head matchup.
If you were to actually write down any set of tie-breaker rules, Ohio State and mutts would be left out. Then the head to head would put Texas over Alabama. There is no possible way to draw up a tie-breaker rule scenario where Alabama wins. The only way is to decide totally subjectively that you want Alabama in. Then you can come up with some kind of argument, but that argument is going to be subjective and not something you could actually write a rule about.