No, something being under github.com/google means the person who started it was paid by Google, not paid by Google to code this. Google contracts (like most tech contracts in the US) have ridiculously broad IP assignment clauses, so unless you go through a lengthy process to request Google disown something, they own anything you code, and they insist you open source your things under github.com/google.

You decide your own definitions, but that's very different from "Gmail by Google" or even "Go by Google" in my book. Note how the main author has "Ex-Google" in their bio, too.