That 33-6 stretch included a 10-3 record in 2010. Utah was invited to the Pac in the summer of 2010 so their 2010 football record had nothing to do with the invite.
In the 3 full football seasons before the Pac invite they were 32-7. The same record BYU had over that same stretch. Just like BYU they had 1 conference championship during that stretch. Just like TCU, Utah spent 28 weeks ranked in the AP poll during that impressive stretch. BYU was ranked for 36 weeks in the AP poll during that same period. They were 1-2 vs. BYU during that time.
Dr. Hill and Kwhitt did masterfully position Utah as the 2nd most respected team in the state which made them a perfect fit for the Pac-12.