Actually now it's become so "Cool" to be part American Indian that people are claiming it when it does't exist. Interesting shift over time from trying to hide that ancestry.
It's even worse for being Irish (the officially sanctioned "cool" ethnic derivation); a lot more people claim Irish ancestry than actually are Irish these days.
The other neat angle is a lot of people who consider themselves "white," particularly in the South, are a fairly substantial % black African (10% or so.)
I remember an article about the topic in Scintific America stating that there is a High percentage of European blood in the black population in America.
Probally a reason some Arabs look like Europeans. The Roman Empire certinaly helped out with Genetic mixing between the populations of Europe and the Middle East and Africa.
Who wouldn't want to be of Irish blood? :) John Kerry claimed it for years......even though he's about as Irish as I am English....none(that I know of)
A lot of the Irish (Orange) particularly from Appalachia are actually the "Scots-Irish" who are mostly Presbyterian and descended from Scottish settlers who first moved to Ulster and displaced the Catholics there.