The argument is not that they are identical. LLMs and diffusion models learning is a new thing. We are all trying to come to terms what that means, and how we should regulate it. (And if at all we should regulate it) Do note, we are talking about here what the law should be, not what the law is.
And in doing so we compare this new thing to already existing things. "It is a bit similar to this in this regard" or "it is unlike that thing in this other regard".
I don't think it is controversial to say that if an LLM outputs byte-to-byte the text of a copyrighted work the work remains under copyright. The person who run the LLM does not magically gain rights by that. If you coax your model to output the text of the Harry Potter books you don't suddenly become able to publish it.
The question is what happens if the new work contains elements from copyrighted works. For example if it borrows the "magical school" setting from HP but mixes it with Nordic mythology and makes it as deadly as Game of Thrones. What then? Can they publish this new thing? Do they need to pay fees to J K Rowling, and George R. R. Martin?
It is generally permissible to publish that new work if it was created by a human. If it is sufficiently different from the other works you are free to write and publish it. Does this suddenly change just because the text was output by an LLM?
The argument is not that "human learning" and "machine learning" is the same. It is that they are similar enough that one has to argue why you think one can create new work and why the other can't.