Consider, however, Teddy and Franklin Roosevelt. They could not possibly be considered as Dutch as Martin Van Buren -- whose first language was Dutch -- but, then, what are they? Anglophile they both were, but they were neither ethnically "English" like Washington nor "Scots-Irish" like Jackson. Mostly, they were just New Yorkers -- though that's not an ethnic label at all.
Then, if we are to go down this road, what are we to say of Ward Churchill, who claims to be Native American, but isn't? Or of Barack Obama, who acquired the identity of "African-American," as commonly understood?
And why does it matter so much, anyway?