SJ is not the “AI” portrayed in the movie her. And AFAIK she does not in fact have all the same idiosyncrasies and tones in real life as the voice does in the movie because she was in fact directed to act like that.
Not only that but the voices are not the same because there was another actress for sky as we have seen.
To me It seems as if the case for SJ is DOA unless it comes out somehow that they in fact trained on her voice specifically. But since that doesn’t seem like the case I have no idea how SJ can legally own all voices that sound like hers.
It would obviously be a different story if OpenAI were saying that sky was SJ but that’s not the case. To me the question should be is “can the studio own the character in her that openAI was copying and any similar things”. Which given that systems like SIRI were already out there in the world when the movie came out and we knew this tech was on the way. The answer should be no but IANAL.
I’m not a huge fan of OpenAI anymore and I think they deserve criticism for many things. But this situation isn’t one of them.
Clarification: Of course if it turns out that they in fact trained on SJ or altered the voice to be more like hers then I’d think differently. I still think the studio has more of a claim though look from the outside and not being a lawyer.
Edit: clarification
It's still Scarlet Johansons voice and acting. The same role with the same lines read by different actors would be very different. Imagine for example that they would have cast Tilda Swinton for Samantha. Even with the same script it would probably end up a very different character. Actors aren't interchangeable.
It's very clear that OpenAI was trying to make ChatGPT sound like Samantha from Her. Whether they used Scarlet Johansons voice to train, or excerpts from the movie, or had writers come up with typical responses that sound similar to Samantha are details, and it's up to the lawyers to figure out whether this is legal or not.
But the undisputable fact is that OpenAI took heavy inspiration from a movie, and did so without permission. You could argue that taking inspiration from a popular movie is fair game, but I'm not sure where the line is between "inspiration" and a blatant rip-off.