As written the headline is pretty bad, but it seems their argument is that they should be able to train from publicly available copywritten information, like blog posts and social media, and not from private copywritten information like movies or books.

You can certainly argue that “downloading public copywritten information for the purposes of model training” should be treated differently from “downloading public copywritten information for the intended use of the copyright holder”, but it feels disingenuous to put this comment itself, to which someone has a copyright, into the same category as something not shared publicly like a paid article or a book.

Personally, I think it’s a lot like search engines. If you make something public someone can analyze it, link to it, or derivative actions, but they can’t copy it and share the copy with others.