I would liken the AI with a photo camera. I can't paint very well, but I can take this miraculous machine and create a picture on the press of a button. Yet there is still artistic expression in deciding when an where to press the button, and at which angle you hold the machine when pressing the button. And we universally agree that whoever pressed the button owns the copyright of the created picture, even if most of the work is done by the machine.
With AI in general and neutral networks specifically the same applies. There's some nuance to decide if the copyright belongs to the person who trained the network or the person who prompted this specific output. The easy solution is to say "both", and let people handle it with copyright assignments and license agreements.
When we have AGI that thinks for itself we might want to rethink this, but that's in the far future.