Justice Story's status as a primary early authority is not a point I dispute. I'm glad you recognize his stature. So let's examine Story's views on the point at issue.
The following is the portion of Shanks v. Dupont I've seen held up in alleged support of a "citizen parent" basis for "natural born citizen."
If Ann Scott was of age before December, 1782, as she remained in South Carolina until that time, her birth and residence must be deemed to constitute her, by election, a citizen of South Carolina while she remained in that state. If she was not of age then, under the circumstances of this case, she might well be deemed to hold the citizenship of her father, for children born in a country, continuing while under age in the family of the father, partake of his natural character as a citizen of that country.
Miss Scott was born before 1776 to English parents on what was then indiputably English soil. What was at issue was her status in the period 1776 - 1782 when the political status of South Carolina was in dispute. Justice Story reasons that if she was of age before 1782, then she had "elected" by her continued residence there to be an American citizen. If, however, she remained under a legal disability (still a minor) then the law views her status to follow that of her father who is deemed to have chosen for her.
But that case doesn't present the question of the status of someone born when the land was indiputably part of the U.S. status to parents who were not then citizens. And that is the question that arises when President Obama or Marco Rubio or Bobby Jibdal is discussed. But there is later a case which presented that very question -- U.S. v. Wong Kim Ark. And, interestingly, Justice Story was cited as an authority on that question:
In Shanks v. Dupont, 3 Pet. 242, decided (as appears by the records of this court) on the same day as the last case, it was held that a woman born in South Carolina before the Declaration of Independence, married to an English officer in Charleston during its occupation by the British forces in the Revolutionary War, and accompanying her husband on his return to England, and there remaining until her death, was a British subject within the meaning of the Treaty of Peace of 1783, so that her title to land in South Carolina, by descent cast before that treaty, was protected thereby. It was of such a case that Mr. Justice Story, delivering the opinion of the court, said:
The incapacities of femes covert, provided by the common law, apply to their civil rights, and are for their protection and interest. But they do not reach their political rights, nor prevent their acquiring or losing a national character. Those political rights do not stand upon the mere doctrines of municipal law, applicable to ordinary transactions, but stand upon the more general principles of the law of nations.3 Pet. 248. This last sentence was relied on by the counsel for the United States as showing that the question whether a person is a citizen of a particular country is to be determined not by the law of that country, but by the principles of international law. But Mr. Justice Story certainly did not mean to suggest that, independently of treaty, there was any principal of international law which could defeat the operation of the established rule of citizenship by birth within the United States; for he referred (p. 245) to the contemporaneous opinions in Inglis v. Sailors' Snug Harbor, [p661] above cited, in which this rule had been distinctly recognized, and in which he had said (p. 162) that "each government had a right to decide for itself who should be admitted or deemed citizens," and, in his Treatise on the Conflict of Laws, published in 1834, he said that, in respect to residence in different countries or sovereignties, "there are certain principles which have been generally recognized by tribunals administering public law" [adding, in later editions "or the law of nations"] "as of unquestionable authority," and stated, as the first of those principles, "Persons who are born in a country are generally deemed citizens and subjects of that country." Story, Conflict of Laws, § 48.
So Justice Story affirms as the rule of law in the U.S. that which I have asserted was the English rule pertaining to "natural born subjects" and which was later incorporated under the lingusiticaly similar term "natural born citizen" -- i.e., that "persons born in a country are generally deemed citizens of that country." Story does not qualify this (nor did Blackstone as to the English rule) with any requirement that the parents be citizens (subjects) of that country.
So it's great that you consider Justice Story "perhaps the greatest authority on the common law and its influence upon us in our early days." So now that I've made clear that he affirms for U.S. the jus soli rule which prevailed under the English common law, are you going to modify your position?
And Mr. Mr. Chief Justice John Marshall also disagreed with you in his concurring opinion in one of The Venus cases.
That portion where he quotes from Vattel C.J. Marsall is writing in dissent (a minor correction). The larger point is to observe that a) his opinion involved the question of domicile in an international law case, b) that citizenship wasn't in dispute, and c) that NO mention of the Constitution nor U.S. rules on citizenship was made. To conclude wrest from his dissent a supposed rule about the Constitutional term "natural born citizen" is one very, very large textual and logical leap.
I had a several round dialogue with DiogenesLamp on the prior Ted Cruz thread (titled "Sen. Ted Cruz Triumphs . . ."). I can pull out all the points and arguments if needed. But you have enough at the moment dealing with J. Story.