why does it matter how it was trained? The question is, does the generative AI _output_ copyrighted images?
Training is not a right that the copyright holder owns exclusively. Reproducing the works _is_, but if the AI only reproduces a style, but not a copy, then it isn't breaking any copyright.
For example facts in the phonebook are not copyrighted, the authors have to mix fake data to be able claim copyright infringement. Maybe the models could finally learn how many fingers to draw on a hand.