No, those words establish that the Framers (in particular, John Jay) were concerned about the “admission of foreigners into the administration of our national government.” By my reading of Jay’s letter, they were concerned about the possibility of a foreigner immigrating to the U.S., becoming a naturalized citizen, and then running for President. Madison (the father of the Constitution) said it himself - in the U.S., place, not parentage, matters.
You, sir, are not intellectually honest, and here’s why:
John Jay first expresses a general concern about foreigners in the administration of the government, which is immediately followed (in the same sentence!) by the words “and to declare expressly that the command in chief of the American army shall not be given to, nor devolve on any but a natural born citizen.” The construction allows of no other intellectually honest interpretation but that Jay was asserting that the explicit requirement that the President be a natural born citizen was the foremost measure that should be taken to prevent foreigners playing any managerial, ministerial or executive role in the administration of the national government.
Again, you lack intellectual honesty.
Firstly, Madison did not say (as you strongly imply) that only the place of birth matters, and that that parentage is irrelevant. What he said was that "place is the more certain criterion," and that place applies in the United States. He did not add "and parentage does not."
Secondly, there are only two legally-supportable meanings of "natural born citizen." One would have it as being the same as the meaning of "natural born subject" as defined in British common law (except for the differences in meaning between 'subject' and 'citizen'), and the other would have it as being what de Vattel defined and then labeled with the words "les naturels, ou indigenes." If its meaning is the same as "natural born subject," then parentage also confers citizenship, not just place alone.
And under British common law, even naturalized citizens had the status of "natural born subjects." "The English common law provided that an alien naturalized is "to all intents and purposes a natural born subject." Co. Litt. 129 (quoted and cited in United States v. Rhodes, 27 F.Cass. 785, 790 (1866)).
Thirdly, US law and court precedents have without exception, from the beginning of the country, recognized anyone born anywhere to US-citizen parents as US citizens from birth, although the person is required, once he becomes an adult, to eventually become a resident of the US and make formal declaration that he accepts US citizenship.
Just from the above alone, the evidence is strongly against Madison having meant what you seem to think he meant. But wait, there's more.
Fourthly, there is also strong evidence against your interpretation from the full text of what Madison said, and the context in which he said it.
He was speaking in favor of the right a man, one Mr. Smith, to be seated in Congress, against accusations that he was not entitled to be a Representative because he was not a citizen. The issue had nothing to do with whether or not Mr. Smith was eligibile to be President, or was a natural born citizen. Madison essentually argued that Mr. Smith was a citizen because of where he was born, and because he was a minor when his parents sided with the British loyalists against the American Revolutionaries. He focused on that point, because he obviously felt that any adult who sided with the British loyalists would not qualify as citizens. Bear in mind the the Constitution allows naturalized citizens to serve in Congress, there is no requirement that one have "birthright citizenship" (whose normative definition means either "jus soli" OR "just sanguinis" citzenship (OR, not AND.))
Give that, to imply that Madison's statement has anything to do with the semantics of "natural born citizen" is not just intellectually dishonest, but highly so.