Earlier quoted context omitted.
“Copy” is ambiguous here. Of course data is copied during training. That said, OP is referring to whether the resulting model is able to produce verbatim copies of the data.
"Of course data is copied during training" is copying. As far as I know, the law is consistent that temporary copies are also covered by the copyright act, and that's how some analogous cases were resolved.
It becomes illegal if I try to distribute those copies
So the question is, does distributing an AI that has been trained on Harry Potter count as distributing Harry Potter?