I'm not familiar with the specific laws that are relevant here, but I have trouble buying the argument that this constitutes a "likeness" when Johansson was in no way involved in its creation, other than by providing inspiration.

So they asked her and she turned them down. But guess what, they can get a pretty good result without even involving her. It turns out that her "talent" for the voice from the movie Her is in fact not so unique and valuable because it can be reasonably well replicated by other people, so why shouldn't a company be able to choose an alternative like that? A person should not have an exclusive claim to the rights of all voices that sound remotely like theirs.