It sort of seems to be true, according to Uber. Specifically, Uber covers driver liability (so it's about Uber and its relationship to drivers, not Uber and the customer: it covers the driver's liability). They maintain $1,000,000 third-party liability insurance and uninsured / underinsured motorist bodily injury. They provide insurance certificates within the US here, and this covers the 50 states plus DC and Puerto Rico. The state of Washington certificate is here, and here is Texas. These are informational summaries, not insurance policies, so the devil is in the actual contract, but it seems to match their online self-representation. The one point that may need to be clarified is that this covers up to $1M of total driver liability, not just passengers.
It's not clear whether an Uber driver can refuse such coverage purchased on his own behalf – you'd have to look at the contract between the driver and the company. Of course the driver has to have liability insurance anyway: Uber simply makes sure that happens, and increases coverage above the statutory minimum.