I'm not sure you're right, legally speaking. At the very least it's a grey area. I certainly have the "reasonable expectation of privacy" (the legal test) in a hotel room that I don't own - a hired car doesn't seem that different to me. When you see an actor get into a car to avoid the paparazzi - they rarely own the car, and reasonably expect the driver not to film them and upload to TMZ or something. (IANAL, TINLA)

Uber cars aren't technically owned by a business like a hotel is though. If you stay the night at my house, there's a DVR system in some of the rooms. Deal with it.

Edit: Also, you probably are being filmed elsewhere in any major hotel (lobby, halls, etc). And I've seen plenty of that footage end up on TV.

Again though, you're not applying the proper legal test. The law isn't "who owns the property you're on" or "is the property owned by a business or individual," it's "do you have the 'reasonable expectation of privacy' on that property?" The former may factor into the latter, but it's not as cut-and-dried as your comments would make it seem.

edit: here's some precedent that may suggest you do have expectation of privacy as a passenger in someone else's car, though the scenario is different http://digitalcommons.tourolaw.edu/cgi/viewcontent.cgi?artic...

There's also another person there. In public you're supposed to find a secluded spot, not sure how much privacy you can expect in that situation.

Technically most hotels don't own their buildings either...

Uber's position is that its ride sharing, and that's why the drivers are employees. Arguing that they have a reasonable expectation of privacy now that it would benefit Travis is just arguing out of both sides of the mouth.

Uber isn't even a public company. How did he become a public figure?

I think its unfair to say that simply by doing business with the general public, every CEO becomes a public figure.