If you read the copyright text on the back of the title page of a book, buying it doesn’t give you the right to “mechanically reproduce” the book. I would be very surprised if there was a court ruling that didn’t either A)completely strike that notice and say it’s fair game to photocopy or scan books you have bought for any purpose (which is not what courts have held in the past, so it would be a big shift) or B)uphold it and say it also applies to scraping the content of a book for training.

…especially given the US “fair use” doctrine takes into account the effect that a particular use might have on the market for similar works, so the authors are bound to argue that the existence of AI that can reproduce fanfiction-like facsimiles of works at scale is going to poison the well and reduce the market for people spending actual money on future works (whether or not that’s true is another question).

So in my view the court is going to say that buying a book doesn’t give them the right to train on the contents because that is mechanical reproduction which is explicitly disallowed by the copyright notice and they don’t fall under the “fair use” carveout because they affect the future market. There isn’t anywhere else where they were granted the right to use the authors’ works so the work is disallowed. Obviously no court finding is ever 100% guaranteed but that really seems the only logically-consistent conclusion they could come to.