You're correct in this particular case, but I want to point out that copyright only protects fat-cat artists. OpenAI and StabilityAI thought training on web text and images was OK, but restricted themselves to public domain & licensable audio, because the music industry is perfectly willing to bleed millions keeping you from kidnapping what they've rightfully stolen. Visual artists and writers generally own their own works, unlike musicians, which means they're on the hook for individual enforcement to the tune of 5-6 figures per lawsuit. There's no mechanism that would allow for someone - even the government - to just step in and enforce copyright over the entire training set.
If, say, someone started writing Ruffle PRs with ChatGPT and filing them as made by "AI kmeisthax", that'd probably be a trademark or publicity rights violation. I'd be furious - but I wouldn't be able to stop them. Not without paying a potentially life-ruining amount of money to pursue a marginal claim in court against some anonymous J.Doe.
Likewise, there's shittons of people who steal art and writing, reselling it on T-shirt stores and Kindle without much in the way of legal recourse. Those are often legitimately lost sales[0], too! And yet, despite having some of the strictest copyright laws in history, artists don't really have the means to shut them down beyond "dox yourself with a DMCA notice". They are starving despite copyright.
Private property is a thing that makes it harder to overconsume scarce resources. It doesn't protect against exploitation. What you want is collective bargaining and enforcement - i.e. a law specifically prohibiting misleading use of AI with rights of action for all parties.
[0] As opposed to, say, arguing that a BitTorrent download is a lost sale