You would be incorrect. USC has 11 National Championships compared to 6 at Tennessee.
Your football numbers are a little off
National poll championships by current conference membership (1936–present)
Conference Championships Schools
Big 12 18 Oklahoma (7)1, Nebraska (5)2, Texas (4)3, Colorado (1)4, Texas A&M (1)5
SEC 18 Alabama (
, LSU (3), Florida (3), Tennessee (2), Georgia (1), Auburn (1)
Big Ten 15 Ohio State (5), Minnesota (4), Michigan (2), Michigan State (2), Penn State (2)6
Independents 10 Notre Dame (
, Army (2)
ACC 10 Miami (5)7, Florida State (2), Georgia Tech (1), Clemson (1), Maryland (1)
Pac-10 9 USC (7), Washington (1), UCLA (1)
Big East 3 Pittsburgh (2)8, Syracuse (1)9
Mountain West 2 TCU (1)10, BYU (1)11
1 Six were won when Oklahoma was part of the Big Eight Conference
2 Four were won when Nebraska was part of the Big Eight Conference
3 Three were won while Texas was part of the Southwest Conference
4 Was won when Colorado was part of the Big Eight Conference
5 Was won when Texas A&M was part of the Southwest Conference
6 Both were won while Penn State was independent
7 Three were won while Miami was an independent and two while part of the Big East Conference
8 Both were won while Pitt was an independent
9 Was won while Syracuse was an independent
10 Was won while TCU was a member of the Southwest Conference
11 Was won while BYU was a member of the Western Athletic Conference (WAC)
I also find it amusing that all the people who talk about the SEC being the best conference, yet it took this current run of national championships to finally tie the Big 12. It all is cyclical and soon another conference will replace the SEC as the most dominant