Absolutely there was variance involved, but it's hard to argue that the quality of teams didn't play a bigger factor. There were multiple major players in the conference at that time. Just look at 2003 for an idea of how strong the conference was. 02 Missouri and 04 Kansas' runs are also an indicator.
Make no mistake, the Big 12 was obviously on the right side of variance, but they were playing with stronger hands as well. That you have the sheer number of teams getting high seeds, while lower seeds advanced further as well is plenty of evidence.
2002 Kansas - (1) F4 (lost to 1-seed Maryland)
2002 Oklahoma - (2) F4 (lost to 5-seed Indiana)
2002 Missouri - (12) E8 (lost to 2-seed Oklahoma)
2003 Texas - (1) F4 (lost to 3-seed Syracuse)
2003 Kansas - (2) CG (lost to 3-seed Syracuse)
2003 Oklahoma - (1) E8 (lost to 3-seed Syracuse)
2004 Oklahoma St - (2) F4 (lost to 3-seed GT)
2004 Kansas - (4) E8 (lost to 3-seed GT)