It is possible to be banned from minecraft multiplayer without doing anything wrong

This is not true. I would recommend you read the Player Reporting page in the Minecraft website so you can understand the player reporting system better. If you are confused about the reasons you can potentially get banned for, head to the "Player Report Categories" section. Otherwise, this is feedback and the bug tracker is not the place for feedback.

But the moderators are humans and humans make mistakes so they can accidentally ban players who haven't done anything wrong. My girlfriend says the easiest solution to fix this bug is to remove chat reporting from the game.