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Not only web sites, full books from scribd and other sources.

Is it legal for one of their computer systems to access mine without my consent, even if publicly routable via the internet?

If I found an open port on a government computer it is still illegal for me to access that isn't it? Is the difference that this is port 80/443 and happens to serve HTTP requests something that has been described in law or court?

see LinkedIn vs HiQ (which HiQ won) covering fair use of logged-out web pages.

I have to log in to OpenAI to generate conversations but the conversations I can post on my own logged-out blog. It's the same thing OpenAI would probably say if they got sued because GPT spits copyrighted content it found on a logged-out webpage. They can't reasonably expect people to not use them for training.