I think more people would be on board if you had left it at "SEC team" or, even better, if you'd have said "Therefore since OSU beat IU aren't we technically the SEC AND B1G Champs?"
We're like the WWE Heavyweight, USA, and Intercontinental Champs at once, unified all 3 belts!
Here's the breakdown:
Nat. Champs = Heavyweight
B1G = USA
SEC = Intercontinental