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?