Long story short, I think you're "probably" right. But the other thing that helped out Auburn was Boise State losing to Nevada. That defeat of an unbeaten made the case easier against TCU, and I surmise you're correct on the complicated BCS formula (a mystery right up there with the WWF "rule book").Maybe Im remembering this wrong so @selmaborntidefan if you have anything to add or correct please do. But I think the 2010 Auburn team would've 100% gotten in with a loss over us and a win over USCe the following week. here is why:
1) With the loss on the road to Alabama that ensures 1 thing, that Oregon will still be the opponent in the NCG since the Pac 12 and Big 10 didn't have a conference championship to make a case.
So here are the teams that would contend for the #2 spot
-Auburn 12-1
- TCU 12-0
-Stanford 11-1 (blowout loss to Oregon in which it wasn't even as close as the score really was. Oregon let Stanford jump out to a 21-3 first quarter lead, and out scored them 49-10 the rest of the way shuting Andrew Luck out in the 2nd half)
-Wisconsin 11-1 (beat #1 Ohio State like a drum but lost a weird game @ MSU)
2) The BCS algorithm would 100% reject TCU and the human voting would totally reject Stanford in a rematch. So it really leaves Wisconsin and Auburn.
3) Auburn having 1 more win with a significantly higher SOS would trump Wisconsin's stellar win over Ohio St.
So why then was TCU ranked #3 in the post championship BCS standings? Because the Rose Bowl was 3rd in the pecking order and didn't have a stipulation to take the #2 team in either the Big 10 or Pac 12. More or less it was giving the Rose Bowl a reason to pick anyone but UConn (AQ from Big East) because everyone knew the Sugar was going to pick Ohio St to play #2 SEC (Arkansas) and the Orange was going to pick Stanford to play the ACC champ Virginia Tech.
Point is, an Auburn loss to Alabama on the road probably changes nothing but the Heisman trophy winner and an undefeated championship. It probably hurts TCU the most because voters are probably scrambling to prevent either TCU and Stanford in getting in. So really the only team that probably benefits from it is possibly Wisconsin, but its highly unlikely that they get in over Auburn.
And in the end it would have come down to the fact Auburn lost to a top ten team, which we would have been had we beaten them.