I can't put my finger on them but I remember reading a bunch of posts where players were discussing getting banned for using FOEHelper back before INNO mandated changes to it were implemented (in particular the disabling of the sniper "helper"). Nowadays, FOEHelper seems to be ignored by INNO but, if a player had not permitted the updates to FOEHelper, I would think that they could still run into trouble for using the old variant.
A lot of people also didn't know there was a difference between FoE-helper and FOE Power Tools.
If you search Forge of Empires in the Chrome Web Store, FOE Power Tools is still the first result.
Also, someone reported FoE-helper once to Google, as some revenge thing (development-related), and Google took the extension down in the store for some time. Most likely some people downloaded Power Tools then as they thought that was the FoE-helper.
It is very possible (most likely) that people falsely reported they got banned because of the FoE-helper. If FoE-helper truly caused bans, a lot of people would've been affected at that time.
Grepolis and Tribal wars allow scrips that are reviewed by the support team, and I've never heard of false bans because of scripts that only read data. And I don't think FoE will have another anti-cheat system than Grepolis or Tribalswars where auto-clicking/cheating has a much bigger impact on the game.