Though most of these cases aren't litigating this. They are charging that the ability to recreate copyrightable material is the fault of the tool and not the tool user[1].
If I measure the length of a song? Not copyright infringement. If I take even a very short sequence of PCM samples, copyright infringement.
But the practical thresholds appear to be different, there's a bunch of ways you can extract kbs' worth of information from a song, some are considered copying (ripping the melody to midi with a converter, say), some are not.
And in the case of "AI", depending on the model it could be extracting and encoding almost anything, because it's a catch-all term encompassing dozens of architectures and methods.
A drop of blood falls in a lake.. which bit of lake now contains blood?
The user is in this case the "AI" company.
They already violated law almost certainly by copying stuff from the net in the first place. (Almost certainly as it by now does not look like this was fair use, and there is no other means to make legal what they did.)
Some people (like the NYT¹) are in fact demanding before curt the destruction of the trained models as they obviously contain copyrighted content.
¹ https://pressgazette.co.uk/media_law/new-york-times-open-ai-...