If you don't take Uber's word for it, don't use Uber. Given that there are alternatives available, I don't see the need for regulation here.
It doesn't always work out this way, but I think in the case of companies like Uber, the interests of the company, the customer and society as a whole all align. To be able to make a profit, Uber needs to be perceived as safe. The most effective way to do that is to actually be safe.