What it sounds like to me, going back to 1994 or so, is the only working relationship Texas had with the northern schools was with Nebraska. In fact, it sounds like they've practically been bed-buddies for 15 years. Together they ruled the Big 12, Nebraska basically being the voice for the entire North. Without warning Nebraska packs up and leaves the conference, and Texas is convinced the conference is dead because they have no working relationship with anyone else in the North. Is that their fault? Of course - they should have been working with us all along instead of just masquerading around with Nebraska. However, because Texas has no history with working with us, they feel that the remaining North schools aren't going to want to work with them now - thus "The Big 12 is dead." Yeah, each of the four schools had individually petitioned Texas to reconsider leaving the conference, but each school did so with the assumption that Texas was already out the door.
When the North schools + Baylor came together and offered the deal that they did, despite the absolute mistrust of the South schools, especially Texas, it showed Texas that the North schools were actually willing to work with them to hold the conference together. It also certainly didn't help matters that Texas was going to be the bad guy in all of this in killing the Big 12 and a 100-year old rivalry with A&M. Suddenly Texas is just happy that the North schools, who historically have never worked with them, are willing to work with them to save the conference, and while they didn't necessarily want all of the buyout money to themselves, it was the goodwill offering that proved to Texas that the North schools + Baylor were serious about it.