I think some people might misunderstand what happens when they report that their account has been compromised/stolen. Riot will put a lock on the account, which will say that the account has been suspended when someone tries to log in, and then a lot of people flip out and think they've been banned because they reported that their account was stolen. When it's just a safety measure that Riot has in place to make sure that the actual owner of the account is the only one that ends up with control over it, and it ensures that the owner contacts support to verify the details. So some of those people might be thinking that they have gotten their bans overturned/appealed, when in reality, they weren't actually banned in the first place. Seems a bit odd, I know, but I've seen it come through the forums many times.
As far as legit ban appeals, the others have addressed that one. Negative ghostrider, the pattern is full.