OpenAI now tries to hide that ChatGPT was trained on copyrighted books, including J.K. Rowling's Harry Potter series

Yes but there's a threshold of how much you need to copy before it's an IP violation.

Copying a single word is usually only enough if it's a neologism.
Two matching words in a row usually isn't enough either.
At some point it is enough though and it's not clear what that point is.

On the other hand it can still be considered an IP violation if there are no exact word matches but it seems sufficiently similar.

Until now we've basically asked courts to step in and decide where the line should be on a case by case basis.

We never set the level of allowable copying to 0, we set it to "reasonable". In theory it's supposed to be at a level that's sufficient to, "promote the Progress of Science and useful Arts, by securing for limited Times to Authors and Inventors the exclusive Right to their respective Writings and Discoveries." (US Constitution, Article I, Section 8, Clause 8).

Why is it that with AI we take the extreme position of thinking that an AI that makes use of any information from humans should automatically be considered to be in violation of IP law?

Not if your stories are transformative of the original work.

Generate your own permutations of the original book into your own story*** and that’s a protected right

yes, but that's a different situation. with the LLM, the issue is that the text from copyrighted books are influencing the way it speaks. this is the same with humans.