Isn't parodies are explicitly excluded from requiring to hold copyright to an object of a parody?
Yes but with complexities in general, and a collision with non-copyright issues for deep fakes that starts to get into more unexplored societal/legal territory. First, parody is part of Fair Use, which means that it's an "affirmative defense": in a lawsuit, the burden is on the defendant to bring it up and prove it. That's in contrast to ordinary defenses or arguments around the facts asserted by the plaintiff, where…
This is a misnomer.
Fair use is an authorized use, and consequently is “distinct from affirmative defenses where a use infringes a copyright, but there is no liability due to a valid excuse, e.g., misuse of a copyright.” Id. Lenz, 815 F.3d at 1152