But it often does. How much do the fans of UNC like Duke and vice versa. Some of the biggest rivalries in the world involve soccer, where actual deaths occur. I'd say that's pretty heated and filled with animosity.
For me, it's Tennessee, South Carolina and Notre Dame. Just because a team isn't going to beat you any time soon (Tennessee) doesn't mean they aren't a rival (to me). The fan bases, in general, dislike each other and some Tennessee fans, at least on message boards, still say very nasty and derogative things about Geno and UCONN. I think no matter what happens, in my lifetime, Tennessee will always be considered rival, no matter how far they (hopefully) fall.
It seems that the more the animosity between the fan bases, the more heated the rivalry. I guess its probably splitting hairs and semantics, but even if we don't play them much, I'd consider Tennessee much more of a rivalry than the 2nd best team in the Big East...