Law dictionaries. Historical references. Even basic word of mouth. It was ALWAYS understood that you had to be born in country of citizen parents to be natural born. It is only since Barack INSANE Obama that we have begun to interject our wishes into the narrative.
If that were true then we wouldn't be seeing all these contentious threads. The fact is that sources as diverse as William Blackstone and James Madison and Roger Taney as well as other lawyers and politicians since them have not defined natural born citizen as you and Vattel do. Why are you right and they wrong?