No one should be allowed to claim they drew something when they didn’t draw any part of it and LLM’s are not people/can’t work without a person. We don’t credit pens and paintbrushes after all.
One could argue nobody should be allowed to claim it. It just exists.
But it didn't just blink into existence.
Even if the person can't claim the copyright of the image produced they ARE responsible for the use of their tools and what they do with the output.
In this case, they released an image with someone else's signature on it. That is wrong, the person should take the blame for that.
The person releasing the image may take it up with the AI service that their tooling led them into making such a mistake. But good luck with that in court...
For the record, the original tweet doesn't explicitly claim anything at all; it just shows the generated image.