Regardless, the answer to your question is the first result when you search Google for "Uber liability coverage":
> Uber holds a commercial insurance policy with $1 million of coverage per incident. Drivers’ liability to third parties is covered from the moment a driver accepts a trip to its conclusion. This policy is expressly primary to any personal auto coverage (However it will not take precedence over any commercial auto insurance for the vehicle). We have provided a $1 million liability policy since commencing ridesharing in early 2013.
If a cab driver in New York City rapes and kills a passenger, it wouldn't make people distrust all cabs in NYC, much less cabs in other cities; there's no brand name to be damaged by news coverage, and as a news story it probably wouldn't even be covered by media outside of the NYC area.
But if an Uber driver rapes and kills a passenger, it will be covered by media everywhere, because Uber is a newsworthy company and because Uber has a global presence, and the Uber brand will be damaged worldwide, not just locally. Because Uber is a "new thing" there will be lots of people/media asking questions about the safety of Uber (in many cases stupid questions, but still).