All this is extremely interesting to see how it will unfold. You know what's also trained on copyrighted material? Real (human) artists! Not only trained but also constantly draw inspiration directly from copyrighted material.
The entire art tradition is based on copying for study, and then using our brains to convince ourselves that we've "transformed it enough" or "my reference is obscure enough that no one will know."
Now we've simplified that process, and more people are exposed to the risk. I hope that the law takes a minute to evaluate the pace of change instead of saying "ITS TOO DANGEROUS, we must BAN IT", but my hopes are low.