Washington was quite clear, and didn't qualify his statement at all. Loyalty to nation overcomes loyalty to locality. Washington considered himself an American, not a Virginian living in America.
That's nice but it doesn't mean beans to an uneducated farmer in the south. Look at how people "belong" to their alma matter. Years after they've graduated they pull for the home team. There were no home teams in 1861, only home locations as indiviual states.
You can quote Washington all you like but it's meaningless in this context.
How utterly noble and principled Washington was to take this stand after he had already led a revolution against "his nation" on behalf of "his locality."