Google's an investor in Uber, it's not difficult to connect the dots - Google is interested in applications of its tech, not in owning the entire stack top to bottom.
Self-driving cars are very certainly the future of Uber, and once self-driving tech is mass-available Uber will have the same accessibility to it that Google or Tesla or whomever else does. At that point, they're competing on price and service quality, just like they do with Lyft and Sidecar right now.
I don't see self-driving tech becoming a major sticking point, because it's not like manufacturers are going to only be manufacturing self-driving cars for their own usage once the regulatory hurdles are cleared.
See some nice photos here: http://qz.com/688003/ubers-self-driving-cars-are-on-the-road...