No, they translated “sujets naturel” as natural born. That is because “sujets naturel” was the French equivalent to the English ‘natural born subject’. Pretty easy to figure out, isn’t it?
They did NOT translate “naturel”, by itself, as NBC or NBS. And Vattel did not write “sujets naturel”.
It is easy to figure out. sujets = subjects and naturels = natural born. So when the founders read "naturels" in Vattel's passage on citizenship, it's PLAIN to see that he was talking about natural born citizenship. Thanks again for proving you are wrong.