Go is imported by Google, not exported by them.
It's also got good funding, a large number of well known core team members (who won't let it die) and a good license which protects the users in the future.
Some other notable organisations develop everything internally and then release it to the public i.e. they export it. For example C#.
More a "solve Google's specific problems" language, general Google purpose
As an example, C++ and Java programs at Google were taking more than half an hour to compile. This is why Go's semantics were chosen with speed-of-compilation in mind:
* Strictly acyclic module hierarchies (greatly simplifies compile-time name resolution)
* No generics (specialization has a compile-time cost)
* Unused imports are a fatal compilation error (to avoid having to parse unnecessary files)
All three of these decisions are somewhat contentious; Pike admits as much in many of his talks. But they were chosen because of the challenges of writing software at Google's scale. It is in this roundabout way that Go "belongs" to Google, in the sense that it addresses problems that Google has and prioritizes the best solutions to those problems, whether or not those solutions are at odds with the needs of non-Google users.
Huh? Cocoa (and the rest of Obj-C libraries Apple does) are just fine, hardly "barely sustained" by the language.
And it wasn't even Apple, the core framework logic is mostly the same as in NeXT era Objective-C (minus some welcomed syntactic sugar additions).
Smalltalk-style OO and C are very well married in Objective-C, and the language has been, historically, a joy to work with. Jusk ask Tim Berners Lee and Carmack.
Even today it gives strengths that other platforms lack, namely the ability to have very dynamic high level abstractions and easily drop to C whenever you want, which for desktop and especially mobile use is very nice: better memory management and no GC pauses, while still having a full blown OO GUI framework.
I can see this first hand with Objective-C, where Apple evolves the language as they see fit. The joining of such different paradigms as Smalltalk-style OO and C was fragile in the first place and can barely sustain the new functionality.
Another example is C#. No matter how nice the language becomes, it will always be the MS language for me, and I don't trust MS when it comes to APIs and languages - they shuffle things around for no reason, cancel projects, etc. And then you're screwed.