The reason why we do appeals in private is that it's hard to tell the context of what's going on and the reason the moderation issued the ban. We usually have people send in reports privately, and we don't want to out people that report griefing, racism, etc. as that opens up them to harassment. With appeals, the person can send us their ID and we can look at our logs to determine what happened.
In this case, it was a moderator's error, and we've resolved it, but oftentimes people will claim they've been banned "for no reason", and our logs show video evidence of them TK'ing or having a racist username, etc.
Manual moderation isn't perfect, and we definitely make errors - what's important is that we correct them.