You raise a good point.
For me, I root like crazy for the Schlecks, of course.
But I don't really care if Martin Mortensen or Robert Wagner get good results, even though they're on the same team.
I guess if no one I was really rooting for was in the race, I'd root for a Leopard.
Unless the team is a quasi-national bunch, like Katusha or Greenedge, I think it's more a case of someone's favorite rider being on the team, than liking the team itself.
Euskaltel, though, might be another exception.