The point is not dual citizenship of parents, it's American citizenship of parents. If Buchanan's parents were American citizens, then he was a natural born citizen.
You are trying to confuse mixed citizenship of parents (one a citizen and one not) with dual citizenship of parents. Even if the parents had dual citizenship, as long as both of them held American citizenship, then the child is natural born.
In this country, we do not have the concept of a blood feud. We do not hold the child responsible for the actions of the parent. If the child inherits dual citizenship because the parent holds dual citizenship through a parent's action, as long as each parent has American citizenship, then the child is natural born. The child is not held responsible for the action of the parent.
On the other hand, if the parent fails to attain American citizenship before having the child, the inaction of the parent descends to the child.
-PJ
What I said was that President James Buchanan was one of three Presidents to have dual citizenship along with presidents Arthur and Obama. That’s all I said.