Sundays, we won't" is "high maintenance", then so be it.
I can see as a likely scenario these Big XII big shots coming in all high-and-mighty thinking that BYU would come, hat in hand, willing to accept any and all terms proffered by the Big XII for an opportunity to be invited. I can see BYU perhaps caving on some of those issues but absolutely refusing to cave on a couple key issues. I can see the high-and-mighty big shots feelings being severely hurt at the rebuff and being offended that BYU didn't cave on every single item. I can see how some would label that "high maintenance" but it is very far from being such - it's simply BYU holding true to some key issues.
OTOH, there could have been several issues that were not all that important that BYU didn't want to agree to which were extremely minor and wouldn't have impacted the core values and standards of the University and the LDS church. In that case, it could more fairly considered "high maintenance".
I don't have any inside info, but I can definitely see my initial scenario not only as merely plausible but even highly likely.