The less cynical answer: they have a business relationship with Uber. They looked at Uber’s logo as they were ordering. Uber took their money. Uber is who appears in their bank statement. They had no control over which driver drives them, Uber did. They had no information about the driver except what little Uber provided them with. If not for Uber they would have never been able to connect with the driver. Uber’s reputation is why they trusted the driver.
> They use minimal vetting on those drivers, and they often look the other way when accounts are rented out illicitly, swapped-in vehicles go unreported, and other hijinks on the driver's end.
Sounds like very good reasons why Uber is liable then?
> How could they possibly even be aware of issues which would affect a driver behind the wheel, or the vehicle on the road?
It also sounds like your very own comment answers this question. By vetting the drivers. By checking the cars. By not looking the other way when accounts are rented illicitly, and so on and so on.