> Inside of a private car with the windows up isn't public.

If it was your car and someone got in and recorded you, then I'd say that's more clear cut. But if you get into someone else's car do you have a reasonable expectation of privacy?

Since you're technically hiring that person and their car to provide you a service, they have to disclose up-front if you're being recorded. In addition, just because you were being recorded doesn't mean the driver has the right to publicize the video. That requires additional consent unless it's a matter of public record.

Dunno about the USA but for the few EU countries I known the law of, the answer is yes, there is an expectation of privacy.

If you go to someone's house, do you expect to be recorded there? I'm not a lawyer, in any case :-).