A poster on a previous thread, GJones2, told me he reads French and after reading Vattel’s paragraph 212 in French said he agreed with my interpretation. Which is to say the same conclusion you have come to; “natural born citizen” means born in the native land of citizen parents.
I’m interested in the phrase “belong to the country”.
Also, I tried here to show that it IS NOT AN OBSCURE REFERENCE, Franklin himself saying that they were consulting it often, often enough for it to influence American law and decisions way before the Constitutional Convention.