I most definately believe that you can still be a fan and become a friend. Like you said, I believe that friendships are made from spending time with the other person, such as on the phone/ internet, eating a meal together, just hanging out and having a good time-- not just greeting at the stage door.
I also think it depends on your personality. Some people get star struck, which ultimately leads to a barrier between any friendship that may have evolved. Others, however, tend not to care the 'status' of anyone, thus creating no barriers and making it much easier to form friendships.
Well, if you are only being their friend because they are a performer, well - I'd rather befriend a policeman...or firefighter. Maybe a dishonest banker.
But still...there will always be the doubt of why you befriended them in the first place.
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