Human creators don't store that 'influence' in a digital machine accessible format generated directly from the copyrighted content though.
Although with the 'good new everyone, we built the torment nexus' trajectory of AI my guess is at this point AI companies would just incorporate actual human brains instead of digital storage if that was the requirement.
Does that imply that if we invent brain upload technology, that my weights have every conflicting license and patent for everything I can quote or create? I don't like that precedent. I have complete rights over my noggin's contents. If I do quote a NYT article in it's entirely, that vould be infringement, but not copying my brain itself.
Your argument boils down to “we don’t know how brains work”, and it is a non-sequitur. It isn’t a violation of copyright law to create original works under the creative influence of works still under copyright.