I think the main issue of contention is just using copyrighted work to train generative AI without the author’s permission regardless.

You must define that in legal terms. This is a lawsuit, after all. It’s not illegal to “just use” copyrighted work. The words “generative AI” are not in a federal or state bill anywhere in the US.

They can have an “issue of contention” all they want, but if they can’t prove anything legally, they have nothing.