I understand this philosophy, but you must understand why many disagree with you.
I, for one, root for a lot of SEC teams in non-conference play. There are exceptions, I will never root for Bama, Florida, or Georgia.
I think you'll find many within the state of Tennessee, and maybe even the southeast in general share your sentiments. However, us displaced fans seem to carry more of a conference pride.
I ultimately think this is because we constantly have to hear how overrated and crappy SEC teams are. Believe it or not, there is not a whole lot of love for the SEC in other BCS team strongholds. I've spent the last few years in Big12 and Pac12 land. Big12 hate for the SEC is other-worldly, and the Pac12 homers aren't too far behind. So it's nice to show up for work the next day after a big non-conference game and hear people come up with new excuses.