Happy 4th of July! In the wise words of Ben Franklin:
The Bald Eagle is a Bird of bad moral Character. Too lazy to fish for himself.
The Turkey is a more respectable Bird, though vain & silly, a Bird of Courage, and would attack a Brit who should presume to invade his Farm Yard with a red Coat on.
Their range also includes Eastern Asia.
Turkeys originated in North America and didn't go beyond that before European colonization.
Also, authoritarians and fascists really love eagles as their symbol even if it's not the bald eagle in particular.
An expansive range doesn't make an animal not indigenous. Also, I cannot find any evidence that Bald Eagles are native to eastern asia at all, I can only find one instance of a bald eagle getting blown over there. The rest of the eagles found in asia are Sea Eagles. The last point is irrelevant.