In the world of Minecraft servers you can't really be falsely banned. Each server is run by their own staff and under their own rules, to which the staff can ignore whenever they please. If someone with access to ban you on a server wants to ban you just for the fun of it, they are allowed. Doesn't make it and less of a legit ban.
Yes I suppose that is true, which is why I don't like to play multiplayer (I play by my own rules :P)
However, there are certainly times where you feel like a ban was unfair or for something you didn't do.