Thaler's assertion seems very short-sighted. If the program/system owns the copyright, who administers that? Is his software capable of granting licenses to allow the art to be published? How did he get permission from it to reproduce the work(s)? How does he even know that it wanted him to register the copyright with the Copyright Office? Perhaps it would prefer that the work was CCO/public domain.

I'm not just being snarky -- I think these are real questions that follow from saying that the system holds the copyright (and I am dubious that he has consistent answers to them).