Perhaps 'strongly suggestive' isn't enough.
https://harvardlawreview.org/blog/2024/04/nyt-v-openai-the-t...
https://www.publishersweekly.com/pw/by-topic/industry-news/p...
No, there have been lawsuits, and the data centers have not been fair game because whether or not the models were trained on copyright-protected works is not generally in dispute. Discovery only applies to evidence relevant to facts in dispute.
Given that everything -- including this comment -- is copyrighted unless it is (1) old or (2) deliberately put into the public domain, this is almost certainly true.
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Many people seem to think that no licence = public domain, but it's still under strong copyright protection. This is the point of things like the Unlicense license.
Yes you could, unless you agreed to forum terms that said otherwise, fair use aside. Its the same in most jurisdictions