False bans do happen. Even VAC, which isn't known for banning willy-nilly, will sometimes remove bans because they do make mistakes. Many other anti-cheats have had more or less prominent issues with false bans, for example GTA Online as well as other games had multiple incidents where they banned people using software like Afterburner/RTSS (and subsequently unbanned them). GTA even had exploits which allowed other cheaters to ban other players.

The sentiment of your comment remains popular in gaming circles. But as software people on hacker news, doesn't it seem rather obvious that complex software like anti-cheats embedded in hugely complex software like games will have bugs? Add many people overclocking their computers to the brink of instability and silent corruption into the mix and you will have issues. (VAC must've kicked me dozens of times for failing game integrity checks because of this - now imagine if that's a ban, like Activision does. A checksum failure on a gaming PC hardly proves cheating beyond even a passing doubt)