There is nothing "official" about The Bitcoin Foundation. They are a private club of people who have decided to give themselves a fancy sounding name and release their own reference implementation of the protocol. Their client is as much a third party client as any other.
I could create my own organization called The Bitcoin Association, and then I could release my own version of the reference implementation. My wallet would be just as "official" as theirs.
As a point of clarification, the reference client is not the Bitcoin foundation's. It's an independent open source project which existed a long before the foundation. The foundation currently funds some of the folks with commit access, though not all, and pays for some resources and tools.
Notwithstanding that, everything else you said was also perfectly fine.