If Google gave them the same access? Essentially opening up all their APIs? That is... Well, unrealistic but also maybe happening more than you realize.Yet Uber would also be amazing if Google gave them that same access, at which point you could chose based on which service is actually better.
Uber, specifically, has strong ties to Google. They use Google maps, and use Google's oAuth (as well as Facebook I think). In general Google as a platform is very permissive.
However, having free reign of Google now and all of Google's user info for example is probably not on the table. For many many different reasons.