Additionally I think you're understating the similarity to the Midler v Ford case. It has a similar pattern where they first contacted the "original", then hired an impersonator. The song wasn't at issue, they had a license to that part.
I think this part of some of the court documents[0] is especially relevant. Hedwig was the sound alike hired.
> Hedwig was told by Young & Rubicam that "they wanted someone who could sound like Bette Midler's recording of [Do You Want To Dance]." She was asked to make a "demo" tape of the song if she was interested. She made an a capella demo and got the job.
> At the direction of Young & Rubicam, Hedwig then made a record for the commercial. The Midler record of "Do You Want To Dance" was first played to her. She was told to "sound as much as possible like the Bette Midler record," leaving out only a few "aahs" unsuitable for the commercial. Hedwig imitated Midler to the best of her ability.
> After the commercial was aired Midler was told by "a number of people" that it "sounded exactly" like her record of "Do You Want To Dance." Hedwig was told by "many personal friends" that they thought it was Midler singing the commercial. Ken Fritz, a personal manager in the entertainment business not associated with Midler, declares by affidavit that he heard the commercial on more than one occasion and thought Midler was doing the singing.
> Neither the name nor the picture of Midler was used in the commercial; Young & Rubicam had a license from the copyright holder to use the song. At issue in this case is only the protection of Midler's voice.
So the fact that us random internet commentors did not recognize her voice doesn't seem to matter in cases like these. It's enough that the sound alike had been told to mimic the original voice, and that people familiar with the voice be fooled.
[0] https://law.justia.com/cases/federal/appellate-courts/F2/849...