The problem with looking at "all championships" is it weights Universities of Virginia's lacrosse and Women's Diving championships from last year the same as Ohio States Football and Mens Basketball championships. There is much more competition for those and most people would agree they mean more.
From a historical perspective... the East schools had a monopoly on declaring a champion for the first 30 years or so. Only since the 1950's has the nation really gotten to play for a championship. The stats on that accord are a bit skewed.
Nonetheless, interesting points. Clearly OU has a pedigree of football... but for all time is far from the race leader. According to this website (which is the most comprehensive I have ever 2 find), they are #7 all time in football:
http://www.cfrc.com/Archives/Top_Programs_2006.htmNotre Dame
Michigan
Ohio State
Alabama
Southern Cal
Texas
Oklahoma
Nebraska
Tennessee
Florida State
The web site explains in detail how the rankings are achieved. The "champions shops" before the coaches and/or AP polls are counted as suspect.