I don't think this is rude at all.
For all you know she could have been nervous about giving it to him. Many people do this when they are nervous about giving something to someone. It's like 'Here, please take it!' and then they quickly run away because they are getting away before they can react, so it's completely normal.
In another sense, it seemed more like the fan was treating him like a janitor by suddenly having him throw away garbage for them without even trying to get his attention that it was a letter.
I understand people have social anxiety and shyness issues, but, at Least have the damn decency to treat him like a human being.
Or the fan could have asked a manager or security team member to pass it along.
And that's what's wrong with society ~ people reveal themselves to be stupid pieces of crap with this type of behavior but think they're still "good".
Did the fan chuck the letter in his face?
It does not matter whether it was chucked into his bag or hit his face. The point was the item was chucked at him. Don't try to nitpick.
If you were him, you would feel upset, too, right? I sure as hell would.