Why does "fair use" even fall into it? I'm not familiar with their specific license, but the general definition of copyright is:
A copyright is a type of intellectual property that gives its owner the exclusive right to copy, distribute, adapt, display, and perform a creative work, usually for a limited time.
Nothing was copied, or distributed (in a form that anybody can consider "The Work"), or displayed, or performed. The only possible legal argument they have is adapting as a derivative work. And anybody who is familiar with how an LLM works knows that the form that results from reading in content is completely different from the source.
LLMs/LDMs are not taking in billions of books and putting them into a database. It is a very lossy process. Out of all of the billions of images trained from the Stable Diffusion database, the resulting model is 4 GBs. There is no universe where you can store billions of images into a mere 4 GBs. Stable Diffusion cannot and will not, pixel-by-pixel, reproduce a Van Gogh. It can make something that kind of looks like a Van Gogh, but styles are not copyrightable.
The same applies to an LLM like ChatGPT. It cannot reproduce entire books, or anywhere close to that. If you ask it to recreate Page 25 of Silverman's book, it can't do it. If it doesn't even contain a minor portion of the original material, it can't even be considered a derivative work.
They don't have a case. They have a lot of publicity and noise, but they will lose to inevitability.