Legally they can take it up with the CC company, not you, and then if they win (they won’t) your CC will charge you.
A quick google search reveals lots more, and none that I saw saying companies can’t come after you for a disputed charge. Most won’t, and most of those that do will only do it if they can clearly show they’re in the right, and you should be able to beat any collection attempt if they aren’t, but they can try.
Prime example: gym memberships