Since the DMCA, just the circumvention of copyright protection measures is a crime. It’s stupid, but the point is that even if training AI on the data is completely legal, if the data was protected with something that is also used to protect copyright, and you needed to circumvent that to get access even for legitimate purposes, you’ve broken a law.
Copyright has been made obtuse and stupid and damaging to society by big IP holders, it’s just now there’s big corps on the “infringing” side too. This will get interesting.