BIG XII has never felt any urgency to finally extend the invite to BYU. They've known that BYU, as an independent, could make the jump at any time with little hangup.
But if BYU joins the AAC, it becomes much more difficult of BIG XII to lure BYU into the fold. The AAC's grant-of-rights, extended contract deals, etc. all make the move way more complicated.
BYU is playing up the possibility of the AAC to make Big XII realize BYU won't stay single forever. Time for BIG XII to put a ring on it, if you catch my drift!