The way I arrive at that is imagine you add just 1 pixel of static to a video, that'd still be a copyright violation. Now imagine you slowly keep adding those random pixels. Eventually you get to the point where the whole video is just static, but at some point it wasn't.
Now, would any media company or court sue over that? Probably not. But I believe that still falls under copy right (but maybe fair use?).
The issue with neural networks is they aren't people. Even when you point your LLM at a website and say "summarize this" the output of that summation would be owned by the website itself by nature of it being a machine transformed work.
Remembered, it's not just mere rote recitation which violates the law, any transformation counts as well. The fact that AI companies are preventing it doesn't really solve the problem that they are in fact transforming multiple copyrighted works into their responses.
What would violate copyright is if you took that rendered page, turned it into a jpeg, and then hosted that jpeg from your own servers. That's the copying that would run afowl of copyright law.