Quick pull of the data for 2005 thru most of 2014 (below | apologize ahead for the table format). I tried to guess the top 15 programs in terms of financial support, recruiting and history plus BYU, TCU and Utah. BYU does have the worst raw winning percentage of the 19 teams listed. BYU also has the least balanced by far, especially since BYU could have only lost neutral site match-ups with ranked teams (based on bowl affiliations the likelihood of BYU's opponent remaining ranked after losing to BYU in a bowl is minimal).

A few other things that I found interesting -

1) Only four teams have winning records against ranked teams: Alabama (22-21), Boise (10-8), Ohio St (20-14) and Oregon (21-19). Based on this year's results I expect that list may drop down to as low as one team.
2) Of those four teams with winning records they are a combined 25-17 in 'neutral' games. Without those 'neutral' games - both wins & losses - no teams break .500 except Ohio St.
3) Teams with similar records to BYU vs. ranked teams: Notre Dame 9-27 (1-4 at neutral sites) and Nebraska 5-29 (0-7 at neutral sites)
4) Only Boise St has played fewer home games than BYU but BSU's schedule is very balanced: 5 at home, 5 on the road and 8 at neutral sites (bowl games). Utah also had a balanced schedule: 13 at home, 14 away, 2 neutral.
5) Most likely to play a top team at home (vs. away | excl. neutral): Texas (64%), Ohio St (56%), Georgia (56%), Notre Dame (55%) and Stanford (54%).

W L H V N Neut. Record
Utah 9 20 13 14 2 1-1
Alabama 22 21 15 15 13 9-4
Oklahoma 20 27 11 19 17 7-10
TCU 13 14 7 14 6 4-2
USC 15 16 13 15 3 3-0
ND 9 27 17 14 5 1-4
Boise St 10 8 5 5 8 6-2
Ohio St 20 14 14 11 11 5-5
Florida 20 29 15 19 15 9-6
Michigan 11 33 19 18 7 2-5
Stanford 16 26 21 18 3 1-2
Auburn 21 29 17 25 8 4-4
Nebraska 5 29 12 15 7 0-7
Florida St 16 22 12 17 10 7-3
Georgia 17 29 15 12 19 8-11
Texas 18 20 14 8 16 9-7
UCLA 16 27 21 20 2 1-1
Oregon 21 19 15 14 11 5-6
BYU 3 22 7 14 4 0-4