Tulane is AAU, that's one of the main reasons they are a big 12 candidate.
People are overthinking AAU vs. Non-AAU.
The Big10 took Nebraska even though they knew Nebby was on shaky ground
The ACC took Louisville
Conference presidents will take schools which can best line their pockets. Four years ago there was alot of options, today there is not. So if conferences are determined to expand, they will "bend" their criteria.
IMO Big12 expansion is going to be contingent on ESPN/FOX agreeing to pay incremental revenue for schools added. The Networks could easily push back as their payments to the Big12 did not drop when the conference dropped from 12 to 10 teams.
I think there could be a compromise, with the Networks paying less than the full $20M for the new schools. Maybe giving the Big12 something like $10M for BYU and UConn and a lower annual payment (like $5M) for schools like Cincy and Houston.