It's not similar at all because you can't get the book back out of the LLM like you can out of Dropbox. Copyright law is concerned with outputs, not with inputs. If you could make a machine that could create full exact copies of books without ever training on or copying those books, that would still be infringement.

> make a machine that could create full exact copies of books without ever training on or copying those books, that would still be infringement.

No it wouldn't. Making the machine is not making a copy of the book. Using the machine to make a copy of the book would be infringment because...you would be making a copy of the book.