Also today I'm writing from what I remember of Blackstone, and I thought he had mentioned a consideration of treason. I could be wrong on that too. Still, the general point is that "natural born" is better read as "born to a natural presumption of whole allegiance".
The sins of the fathers.
Compare to:
"Fathers shall not be put to death for their children, nor children put to death for their fathers; each is to die for his own sins." [Deut. 24:16]