That's completely backwards. Red Sox fans don't cheer for the Yankees in the postseason because of "American League East pride." Think any Steelers fan is rooting for the Ravens in the postseason?
Eh...even though I detest a lot of the "my favorite team is the SEC" types even I can see the weak logic at work here. In the NFL there is no recruiting, no rankings, national perception doesn't matter, etc. I can see why in CFB it is in a team's best interest to have their conference be perceived as strong. Look no further than the preseason rankings every year or the poll from earlier this year when 10 SEC teams were ranked for proof of this. Was Auburn ever really a top 10 team? Hell no, but the teams that whoop their ass benefit from the perception that they were, that bounce in the polls is invaluable.
Look at the Gators, I'm a Florida fan on the side due to marrying into a clan of UF lovers, but do they really deserve to be ranked? Would a team with a similar resume from the B1G or the ACC be ranked? Not likely, yet Ole Miss now gets to go on the road and face a ranked opponent. So, I'm on board with teams wanting their conferences to be strong.
What I'm not on board with are fans of other programs thumping their chests at other teams and acting like Alabama winning the NC meant they won it too. I already didn't like UGA fans, but their behavior after the 2012 NCG cemented my intense hatred for them. They were jumping around like they won the title and talked far more s**t than the Alabama fans. Alabama fans were actually pretty cool. I guess they knew how to "act like they've been there before," whereas UGA fans (having not "been there" in 35 years) did not.