I mean, why not actually compare the voices before forming an opinion?
https://www.youtube.com/watch?v=SamGnUqaOfU
https://www.youtube.com/watch?v=vgYi3Wr7v_g
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Whether you think it sounds like her or not is a matter of opinion, I guess. I can see the resemblance, and I can also see the resemblance to Jennifer Lawrence and others.
What Johannson is alleging goes beyond this, though. She is alleging that Altman (or his team) reached out to her (or her team) to lend her voice, she was not interested, and then she was asked again just two days before GPT-4o's announcement, and she rejected again. Now there's a voice that, in her opinion, sounds a lot like her.
Luckily, the legal system is far more nuanced than just listening to a few voices and comparing it mentally to other voices individuals have heard over the years. They'll be able to figure out, as part of discovery, what lead to the Sky voice sounding the way it does (intentionally using Johannson's likeness? coincidence? directly trained off her interviews/movies?), whether OpenAI were willing to slap Johannson's name onto the existing Sky during the presentation, whether the "her" tweet and the combination of the Sky voice was supposed to draw the subtle connection... This allegation is just the beginning.
Asking for her vocal likeness is completely in line with just wanting the association with "Her" and the big PR hit that would come along with that. They developed voice models on two different occasions and hoped twice that Johannson would allow them to make that connection. Neither time did she accept, and neither time did they release a model that sounded like her. The two day run-up isn't suspicious either, because we're talking about a general audio2audio transformer here. They could likely fine-tune it (if even that is necessary) on her voice in hours.
I don't think we're going to see this going to court. OpenAI simply has nothing to gain by fighting it. It would likely sour their relation to a bunch of media big-wigs and cause them bad press for years to come. Why bother when they can simply disable Sky until the new voice mode releases, allowing them to generate a million variations of highly-expressive female voices?
From elsewhere in the thread, likeness rights apparently do extend to intentionally using lookalikes / soundalikes to create the appearance of endorsement or association.