"and more bowl wins than BYU."

Utah has 13 bowl wins, BYU has 12

Utah has only gone to 17 bowl games ever. BYU went to 17 consecutive bowl games from 1978 - 1994 and 30 overall in their history. A good portion of those bowl games occurred back when bowl games were a true reward for a very good season. Not like today where almost every 6-6 team gets to go. This also often meant playing top competition that also had a stellar year themselves.

Growth of bowl games 1930 - 2010

Year	# of games       Utah   BYU
1930	1                 1-0   0 
1940	5                 0     0
1950	8                 0      0
1960	8                 1-0   0
1970	8                 0     0-4
1980	15                0     5-5
1990	19                2-3   2-5-1
2000	25                8-0   3-3
2010	35                1-1   2-0

Nobody can take away Utah's bowl winning streak or their very good record in bowl games, but back when there were very few opportunites they weren't good enough to go. They also were over looked several times in favor of the bowl (or better bowl) taking BYU instead of Utah. I had a pretty long post about BYU/Utah rivalry a while back that had some pertinent detail in it that I'm including below: http://www.cougarboard.com/board/message.html?id=5692965

Bowls information for those 48 years
28 - Utah times bowl eligible (at least 6 wins)
14 - Utah bowl eligible but no invite
14 - Utah bowl games (11-3 record)

Number of times Utah in bowl games as conf champ/top representative (3) - means better bowl/tougher competition

38 - BYU times bowl eligible (at least 6 wins)
10 - BYU bowl eligible but no invite
28 - BYU bowl games (10-18 record) [17 straight from 1978-1994]

Number of times BYU in bowl games as conf champ/top representative (20) - means better bowl/tougher competition

This was over 2 years ago so some numbers have changed but it helps paint a much more detailed picture than your stats.