I'm an Android developer, so that experience colors my perception. But compare Apple and Google in mobile. Everything Apple comes up with goes into making their product better, and they will fight with every tool they have to make the iPhone the better smart phone.
Every time Google comes up with a high quality product (Google Now, Inbox, Maps), they do everything they can to ship it on iOS as well as Android. If it wasn't for Apple, Google Now & Maps would be just as good on iOS as on Android. Google doesn't use their cloud service advantages as a weapon to make Android better than iOS. They just want their technology in front of everyone, no matter what they use.
I see self driving cars as a similar market. Google wants self driving cars to happen. There are lots of good reasons, but from their perspective it is both a play for even more data, and it increases the amount of time we have to use Google products. I can look at ads even longer if I don't have to drive on my commute. Thus for them doesn't it make sense to license/give away all of that tech to everybody? It doesn't matter who manufacturers the car, so long as it uses Google's car software.
Thus, plenty of companies will make self driving cars using Google's software. Thus Uber will have plenty of access to self driving cars.
If Google was more focused on killing Uber, they would hoard the self driving software for their 1st party initiative. I imagine if Uber invents self driving tech, no one else is getting it. They are far more interested in the core product of driving people from A to B.
It's a bit of 'commodize your compliments' and the two companies respective business model. Google operates a scorched earth campaign of making everything around ad supported internet as cheap or free as possible. Uber and Apple are building businesses around charging money for the product they make directly.