The US Copyright Office says: "The crucial question is “whether the ‘work’ is basically one of human authorship, with the computer [or other device] merely being an assisting instrument, or whether the traditional elements of authorship in the work (literary, artistic, or musical expression or elements of selection, arrangement, etc.) were actually conceived and executed not by man but by a machine.” U.S. Copyright office, Report to the Librarian of Congress by the Register of Copyrights (1966)."
While the dividing line is fuzzy, it is clear that as soon as you're claiming that the art was generated by AI, you are fighting an uphill battle to get a copyright registered.
Again, I am not a lawyer.
Which leads to the conclusion that at least in some cases,a human doing some setup is not enough to grant a copyright.
While this case was partly about the question "can a Monkey own a copyright in a selfie it creates?", I think it got a lot of press because it was so obviously related to the case of AI-created art. If one non-human can get a copyright, why not another? The US Copyright office has shot them both down, on the grounds that only humans can get copyrights.
In the monkey selfie case, the photographer set up the camera, which meant that there were some very abstract settings that involved a human. That wasn't enough to get a copyright. I think at least some hyperparameters would be similar - not really enough to justify creativity.