Since you trust Blackstone as a source, let's see what he had to say about "natural born" and "common law"
So Blackstone schools you on the common law and "natural born." He is very clear here as to what common law says, and it does not agree with the opinions of De Vattel. As you say, read it, understand it, learn from it.The first and most obvious division of the people is into aliens and natural-born subjects. Natural-born subjects are such as are born within the dominions of the crown of England, that is, within the ligeance, or as it is generally called, the allegiance of the king; and aliens, such as are born out of it. ...
When I say, that an alien is one who is born out of the king's dominions, or allegiance, this also must be understood with some restrictions. The common law indeed stood absolutely so; with only a very few exceptions: so that a particular act of parliament became necessary after the restoration, for the naturalization of children of his majesty's English subjects, born in foreign countries during the late troubles. And this maxim of the law proceeded upon a general principle, that every man owes natural allegiance where he is born...
The children of aliens, born here in England, are, generally speaking, natural-born subjects, and entitled to all the privileges of such.
To encourage also foreign commerce, it was enacted by statute 25 Edw. III. st. 2. that all children born abroad, provided both their parents were at the time of the birth in allegiance to the king, and the mother had passed the seas by her husband's consent, might inherit as if born in England: and accordingly it hath been so adjudged in behalf of merchants. But by several more modern statutes these restrictions are still farther taken off: so that all children, born out of the king's ligeance, whose fathers were natural-born subjects, are now natural-born subjects themselves, to all intents and purposes, without any exception; unless their said fathers were attainted, or banished beyond sea, for high treason; or were then in the service of a prince at enmity with Great Britain.
IOW, the universal law of nations that was incorporated into the common law was NOT a limitation on common law. Therefore, it does NOT disagree with Vattel, it simply shows that statutory law was augmented beyond the natural law that formed the foundation of common law.
Further, let's look at how Blackstone defines natural-born in relation to the children of aliens:
The children of aliens, born here in England, are, generally speaking, natural-born subjects, and entitled to all the privileges of such. In which the constitution of France differs from ours; for there, by their jus albinatus, if a child be born of foreign parents, it is an alien.
IOW, Blackstone is clearly saying that this is an exception in England (which obviously goes beyond the natural law). Further, Blackstone says "generally speaking" as in not ALL children of aliens. One of the exceptions is explained in the passage on denizenship:
A denizen is an alien born, but who has obtained ex donatione regis letters patent to make him an English subject: a high and incommunicable branch of the royal prerogative. A denizen is in a kind of middle state between an alien, and natural-born subject, and partakes of both of them. He may take lands by purchase or devise, which an alien may not; but cannot take by inheritance: for his parent, through whom he must claim, being an alien had no inheritable blood, and therefore could convey none to the son. And, upon a like defect of hereditary blood, the issue of a denizen, born before denization, cannot inherit to him; but his issue born after, may.
The "inheritable blood" is what prevents the child of an alien from being a natural-born subject. It only becomes inheritable AFTER an alien goes through denization. Blackstone makes distinctions that are not too dissimilar from what happens in the U.S. when the children of aliens who are naturalized will the become naturalized.
There is also a clear principle explained by Blackstone that was completely rejected in the United States relating to natural-born and common law:
For it is a principle of universal law, that the natural-born subject of one prince cannot by any act of his own, no, not by swearing allegiance to another, put off or discharge his natural allegiance to the former: for this natural allegiance was intrinsic, and primitive, and antecedent to the other; and cannot be devested without the concurrent act of that prince to whom it was first due.
In Wong Kim Ark, they clearly explain what the American position was on putting off "natural allegiance."
by our law, as solemnly declared by Congress, "the right of expatriation is a natural and inherent right of all people," andany declaration, instruction, opinion, order or direction of any officer of the United States which denies, restricts, impairs or questions the right of expatriation, is declared inconsistent with the fundamental principles of the Republic.
Now, why are we to presume that common law would comprehensively define citizenship in this country when we firmly rejected the CORE principle that was used by Blackstone to define "natural-born"??