Nobody takes issue with the idea that a person born on US soil of two US Citizen parents is a Natural Born Citizen.
However, Bingham NEVER states that those born of Citizen parents on FOREIGN soil are NOT Natural Born Citizens, does he?
And why would he bring up that issue? He is dealing with slavery and the citizenship of former slaves, in the United States. Slaves born in other countries were hardly an issue to Bingham, at that time, since the slave trade had ended long before the Civil War, and the 14th took care of that issue in other ways.
Logic, man, logic, and ENGLISH language comprehension.
The bottom line is Bingham reveals that if you have a parent that has allegiance to another sovereignty besides the United States, you are not a natural born Citizen. His statement is perfectly logical.