Yup.....
Therin lies the disagreement. This disagreement dated back pre-founding to English law of allegiances to the King.
Thankfully we don’t have a King and we did not adopt that language, although various legal analysts often bring it up.
This has much to do with original intent and there is a historical string of decisions that will confirm it and that the law of nations and such pre-constitutional law was not the intent.
You’re making a mistake bringing up the Law of Nations.