The original complaint alleges that the training process requires copying the material into the model and thus requires consent of the copyright holder. (Copyright protects copying but notably not use, so the complaint has to say they copied it in order to have standing). Then it says they didn't have consent.

They also mention Books3, but they don't appear to actually allege anything against Meta in regards to it and are just providing context.

I don't think it actually changes anything material about this complaint if Meta bought all the books at a bookstore since that also doesn't give you the right to copy the works.

The original complaint is 2 years old though, so I don't really know the current state of argumentation.

https://www.courtlistener.com/docket/67569326/1/kadrey-v-met...

Note that incidental copying (i.e. temporary copies made by computers in order to perform otherwise legal actions) is generally legal, so "copying" in the complaint can't refer merely to this and must refer more broadly to the model itself being a copy in order to have standing.