Any concern about Uber drivers is mostly unfounded, especially when you consider the creeps the drive regular cabs.
All Uber drivers undergo a background check and must undergo an annual car inspection. Proof of insurance and a drivers license is also required. When you hail an Uber, you're given a picture of his car, his license plate and a picture of the driver, lest you have any concern about being picked up by an ax murderer.
Anecdotally speaking, every Uber car I've ever been was a helluva lot better than some beat to crap old Crown Victoria most cabbies drive.
And as that article notes, there's a huge paper trail involved. It's certainly not an easy avenue to perpetrate crime.