People say this as if the entire (or majority) of Android's success rests with what they initially purchased. In my opinion it has very little to do with that and a lot more to do with the billions of dollars invested into developing, extending the platform, creating and supporting APIs, establishing contracts with OEMs, developing apps, etc etc. Android wasn't some magic thing that anyone that purchased it would have been sure to be successful. Just look at how well MS did with Nokia's purchase.
So yes, Google did purchase Android but Google didn't purchase their mobile success story by purchasing Android.
The whole way that Google handled Windows Mobile was anti competitive imho.
They prevented Windows Phone users from being able to access Google Maps by checking User Agents.
They didn't release a native Youtube app for Windows phone, and when Microsoft wanted to make one themselves they restricted them to HTML5 and non-native access. This penalized battery life on Windows Phone platforms for 2 very large and important services.
Google got success with Android by frankly bullying every other viable competitor out of the market (Amazon Fire, Windows Phone) by again bullying in regards to play store services.
You realize that Amazon Fire is Android, right?
Didn't GMail start as a 20% project?
I don't know about Gmail, but Google Maps was originally one.
They bought Android in 2005, Youtube in 2004? and all of their other, non-search successes.