I have always viewed the concept of being a fan as a purely internal creation, if that makes any sense. I think there are people, of all fan bases, who will use the teams they root for to empower themselves in certain settings, as if there is somehow a personal gain in rooting for a better team than the guy next to you.
You'll definitely see some of that as it relates to fans of college sports (i.e., how can you be a fan if you didn't go to UConn?), and I guess in a certain respect it's fair. If you're a student at a school, you're inherently associated with that school, and by extension its sports programs. Then again, somebody like me who doesn't go to the school but spends hundreds of dollars per year attending games, drives TV ratings, and spends most of my time trying to convince everybody within earshot that UConn basketball is the greatest invention in human history probably merits a certain claim to the school, too.
But I'd define a fan as somebody who devotes a reasonable portion of their time/resources to something without expecting anything tangible in return. Somebody else's definition may vary, but I think people who say things like, "you didn't go to UConn, so you can't be a fan" might want to step-back and reexamine their own attachment to whatever it is they're rooting for. Are you a fan because you like to talk trash to your co-workers, or because you genuinely enjoy supporting whatever it is you're supporting? If somebody else challenged my fan hood, I wouldn't be too defensive, because it just doesn't bother me much. As much as I wouldn't mind being associated with the school/program, my enjoyment of the product wouldn't really be compromised without it.