The NCAA is free to choose the NCAA field how it wants, but I am guessing Alabama could have a separate lawsuit avenue available if the NCAA had no reason to exclude them and just made a "No Alabamas" club. (South Alabama is fine, it's a no Alabamas club... for the Simpsons fans of the forum). And they still could probably argue it was downstream punishment of the team.
The committee would presumably need reasons if they were very clearly in the field by all objective metrics and bracketologies. Alabama isn't on the bubble. You also can't change the selection criteria halfway through the season when there are millions of dollars on the line.