You are assuming the moderators are not lying. Unfortunately, mods on some sites do lie and do claim innocent posters violated rules. I myself was temporarily banned on one site because I argued that the Epic game store was good for competition and would help bring down prices for both consumers and game developers.

The stated reason for the banning was something like “trolling”. Not much to say other than some mods are good but some abuse their power.

Lobste.rs has an open moderation log: you can see what was done by who. It's one of the few places where I think it's possible to actually trust the moderators are treating things fairly.

I will handily take the mods side of the story, it’s quite clear from the effort put in the respective comments, and the underlying incentives (what would a mod win from making up such a complicated story, vs that of the offender party?)