I don't believe that is the case. UT is a Brand Name Program, a ratings magnet, and commands the attention of at least two of the largest TV markets in the US. They have a legion of Alumni and T-Shirt fans all over the Nation, and thus commanded their destiny to a large degree. TCU, or Vanderbilt for that matter, has none of those advantages. A "Great West Conference" marketed with UT and OU in the East, and USC, UCLA in the West would have been a dandy foil to the "Greater SEC." But, alas...
I don't think UT had much say in the matter. They were probably made a suggestion, or, "an offer he can't refuse." The SEC was probably made a nice offer as well. No way this happens without prior approval of the people with the checkbook. In the end, all the Collegiate parties are simply pieces being moved about on a board.
I believe ESPN/Disney is simply hoarding all the Big Players and telling the Streamers to go and pound sand. They have the SEC under contract, probably for a good long while, and they are expanding the property they own. They also own the Playoff, and thus, control the Game in it's entirety for the next few years.