I think this is insightful, based on my own experience. I think the two traits are orthogonal. I'm naturally(?) extraverted, but have always been shy and am still anxious in most social situations.
People would probably recognize me as extraverted, but it requires something like mental/emotional gatecrashing (or some disinhibiting agent).
But I agree with socially confident introverts.
I guess you can have more reasons to behave a given way, and it's really hard to isolate traits or narrow them down towards a definition.