Like most things in life, despite what many liberals or conservatives, Christians or atheists (any other dichotomy you prefer), will tell you, the world is not always black-and-white. Such is the same with the matter of whether or not to pull for the SEC. The answer is probably somewhere in the middle.
On the one hand, pulling for every SEC team against OOC does not directly correspond with the success of your program in any given season, especially if your own team (UT) has been having little success. Making a direct connection is a fallacy, proven even more so by the fact that UT has had its worse stretch while the SEC has had its best. Such a direct connection doesn't hold up under specific scrutiny in any given season.
On the other hand, you don't want every SEC team to consistently tank against OOC (doing so would only weaken your SOC/seeding/etc.). A consistently weak SEC could hurt your own team in the long-run.
So, to end the great debate, let's just say that both sides are partially right.
I still hate Alabama though.