They want nothing to do with the Cats in the Championship Game, for obvious reasons. Look how the mighty Nubb has done against UT since the Big 12 was formed:
12-07-1996 Nubb loses 37-27
Big 12 Championship Game
10-31-1998 Nubb loses 20-16
Lincoln, NE
10-23-1999 Nubb loses 24-20
Austin, TX
12-04-1999 Nubb WINS 22-6 (last Nubb Big 12 titles and last Nubb win over UT)
Big 12 Championship Game
11-02-2002 Nubb loses 27-24
Lincoln, NE
11-01-2003 Nubb loses 31-7
Austin, TX
10-21-2006 Nubb loses 22-20
Lincoln, NE
10-27-2007 Nubb loses 28-25
Austin, TX
That's a lovely 1-7 for Nubb vs. UT overall, 0-6 during Conference play and 1-1 in Big 12 Championship games. Though it may seem like thousands of years ago, don't forget that Nebraska used to have a pulse and be relevant in college football. I know, hard to believe.
On the flipside KSU is 4-2 vs. UT (2-1 in favor of KSU in both in Manhattan and Austin)....and of course 3 of the 4 KSU wins were blowouts.