You really don't have much proof-wise. People rant on here too often about these things for anyone to believe what you are saying without some form of proof. 'Not remembering' really isn't an excuse; if the issue really bothered you that much, you would be taking screenshots. And word-of-mouth isn't exactly reliable either, everyone will always say they did nothing wrong in these situations. The difference being, the people who were banned have some sort of evidence against them that clearly shows they deserved it.
I'm somewhat sick of these rants as well. I have yet to see any form of this 'power abuse' you talk about. In the end, you can choose to believe what the people being punished/banned are telling you, or you can believe the system that is in place to deal with rule-breakers and hackers.