"Of course data is copied during training" is copying. As far as I know, the law is consistent that temporary copies are also covered by the copyright act, and that's how some analogous cases were resolved.
FWIW the essence of copyright law AIUI is: copying is not permitted, unless done in a form explicitly allowed by the license holder.
This scenario seems quite contrived but is there an actual court precedent allowing it? I'm 100% confident no one will ever prosecute you for doing it but that's not the same thing as "allowed".
This case was about pointing <recording equipment> at <content someone is allowed to access> and making a copy to transmit it to <only that person>. The Supreme Court held it to be illegal. There was a lot of money on the line, which is why it went so far.
> there is also a principle that you can have ephemeral copies as part of handling and processing the work.
I'm not aware of this principle. Where is it spelled out?
> Also the result of that case was self-contradicting
I agree the verdict was a travesty. An innovative business went to ridiculous lengths to stay on the right side of the copyright mafia (data centers with tiny individual TV antennas for each subscriber FFS!) while providing a better product and experience. They still had the hammer brought down on them.
> I'm not aware of this principle. Where is it spelled out?
Well, do CDs give you a license agreement that allows you to copy the data? I've never seen one. And it's nearly impossible to play a CD without that copying.
> And it's nearly impossible to play a CD without that copying.
Exactly. It's how you are supposed to use the CD. That's not true for your example of a book on a webcam. You're supposed to read the book, not an image of the book.
That's not the same thing as copying for "processing".
This is not correct. It's only true that no one will go to the effort of prosecuting you for keeping photocopies of books in your home. But copyright law doesn't allow you to do it.