It doesn't matter whether you agree with the chart or not. It is an accurate representation of what "natural born citizen" does and does not mean, as stated by every single real authority in the entire history of the United States.
Use the keyword, "NBC", and read the multitudes of threads posted here, which back up my assertion.
I've read those threads, and a lot more besides.
Here is a revised version of the chart, with a comment regarding Vattel at the bottom:
I'm sorry, but I still disagree with your assessment of that chart. I've done enough reading on the subject to know that it's at odds with the Framers' understanding of the phrase, Natural Born Citizen.
Simple logic dictates that a person born on the soil of a country, to two citizen parents, will most likely have the greatest degree of unshakeable loyalty to the country of their birth. This is the fundamental point here, and is something which I believe the Framers easily processed with simple reasoning.
Further, I firmly believe that it was their intent to encode that simple logic and reasoning into our Constitution, in Article II, Section I of that document.
Using your understanding of the NBC clause, it would be just fine with the Framers if we put a man in the Oval Office who was raised outside this country and its history and culture, simply because he laid claim to having been born on our soil.
Wait.....oh my....we did that in 2008, didn't we?
I think you have done something similar with your graph. It simply says what you want it to say because it's based on your whim. It is proof of nothing.