sources.
There were never any negotiations with the Big 12. Did we respond to requests for information? Yes. Negotiations as in back and forth? None. End of story.
And knowing significant boosters to Big 12 programs, I assure you that in 2010-2011 they did not want BYU and the Sunday play headache that full membership (the only option under consideration at that time) would create. Of course, Sunday play would only affect the Olympic sports, but that made it a bigger issue, not a smaller one. Those programs and their ADs want all of the limited TV exposure available, and eliminating Sunday games with BYU, or worse, cancelling a televised conference tournament game if BYU made it that far, was a headache they (and their TV partners) could do better without, especially when they had other options that did not have such a restriction. Going with TCU and even WVU were easy choices from that perspective.
Sunday play was and continues to be a non-starter with the Big 12, and probably with any other P5 conference. Until football-only membership (or perhaps with Mens BBall) is considered an option by the Big 12, we are stuck where we are.
Your source either received bad or incomplete info, was pulling your chain, or you totally misunderstood. Check again. If your source downplays the import of Sunday play, then I can tell you outright that you received bad info.