Right, but a quick search also turns up numerous stories of traditional taxi drivers attacking/abusing passengers. I think it would be interesting to see statistically significant evidence that one model is demonstrably safer than the other.
I had a family member attacked by a cabbie. He was actually mere hours away from getting away with it too because a) The passenger had no record of the transaction and b) The cab service recycles their camera data every few days.
The way I see it, there is no guarantee of safety in either situation. You never know if your driver is a criminal or crazy. But services like Uber seem considerably more safe: There is extreme record keeping, user ratings, and no direct money changing hands.