The Big XII will try and protect itself from further raids and coerce (or try) the remaining teams to sign up for long term deals, TV right deals, and verrrrry expensive exit clauses should another university try and bolt. So...if they invite BYU, they will shackle BYU with verrrry stringent rules and regulations about leaving the conference and make it financially unfeasible to do.

On the other hand, BYU will try and protect itself from the conference being further raided and BYU being left with the scraps and will want an exit clause should that happen so that BYU can best take care of it's own interests.

Which leads me to believe that BYU will not join the Big XII. Just my gut feel.