That is an interesting question. There is no real way to make sense of this move by Missouri. My guess is that they were still talking during the renegotiating and signing of TV rights, and that while I believe Deaton chaired the Big12 expansion committee, Missouri was still in talks with SEC about joining them. Those are some huge things to try and explain away, especially under oath in a court of law. And I can almost guarantee there are trails, such as emails or phone records that would come up in legal discovery.
So essentially, Mizzou probably tried to be too cute by half, and ended up having to leave, because they had already done enough that there was no backing away from it, and they had already built up the instability excuse, which they were instrumental in creating and continuing.