Nothing about citizenship at birth mentions naturalization. Nothing about naturalization covers those born as citizens.
One is either born a citizen or one must be naturalized.
Those are completely false statements as shown by the evidence I've already given of the Royal Decree and the Acts of Parliament.
Lord Coke for example in his 1608 Report page 208 described a subject born, meaning a natural born citizen.
“There be regularly (unless it be in special cases) three incidents to a subject born. 1. That the parents be under the actual obedience of the King. 2. That the place of his birth be within the King's dominion. And, 3. The time of his birth is chiefly to be considered; for he cannot be a subject born of one kingdom that was born under the ligeance of a King of another kingdom, albeit afterwards one kingdom descend to the King of the other.”
Lord Coke categorized three methods by which a person who was not subject born could be subject made: 1. statute, 2.naturalization, and 3. denization. Four years earlier in 1604, the House of Commons wrote:
“To place the Children, born within this Realm, of foreign Parents, in Degree for the first Birth or Descent only, as Aliens made Denizens, and not otherwise. (House of Commons Journal, Volume 1, 21 April 1604)”
Lord Coke categorized such children as statutory subjects and subjects made. He expressly excluded such children from being subjects born.
The House of Commons could not be more explicit about the true meaning of a natural born subject in English usage stripped of any courtesies used out of context of the true definition. The House of commons in 1604 made it explicit that the child of alien parents was alien made a denizen at birth. Lord Coke chose to describe the method used by the House of Commons as a statutory subject and subject made. Lord Bacon described the method as nauralization.
“Furthermore as the law of England must favor naturalization as a branch of the law of nature, so it appears manifestly, that it doth favour it accordingly. For it is not much to make a subject naturalized by the law of England: it should suffice, either place or parents. If he be born in England it is no matter though his parents be Spaniards, or what you will: on the other side, if he be born of English parents it skilleth not though he be born in Spain, or in any other place of the world. In such sort doth the law of England open her lap to receive in people to be naturalized; which indeed sheweth the wisdom and excellent composition of our law ... (Bacon, Francis, pp.664-665)”
The historical record demonstrates your statements could not be more wrong. The Latin doctrines however named were embodied in the acts of governments, and the governments of England, France, other European jurisdictions, and the United States either did not confer subject status or citizenship status to the a child domestic born with alien parents, or did so by a method variously styled as denization or naturalization. They then sometimes styled the child as a natural born citizen as a matter of courtesy despite not actually being a natural born citizen or being subject born.
Like spelling, terminology in the earlier centuries was often fluid, with duality or multiplicity of definitions in different context even more so than today. Understanding the meaning, then as sometimes in today's world, requires an understanding of the context in which the terminology is used. In the local context of the 18th Century in which the Constitution was written, the meaning of being an alien, foreigner, or stranger could mean a person whose birth and domicile was less than a mile outside the city boundaries or the border of the borough. Nonetheless, the meaning of an alien or a foreigner was used quite differently when determining whether or not a person was a subject or a citizen of the nation, because the terms of alien, foreigner, and stranger were used in the international context. This fluidity in terminology still exists today with respect to a nation like the Netherlands, which has no national citizenship. In the international context people think and speak in terms of Dutch nationality. In reality, however, there is no dutch citizenship, because the Dutch people are citizens of their respective cities and other jurisdictions within the Netherlands which has no national citizenship except in the collective sense.
With respect to the meaning of the natural born citizen clause, the context of the natural born citizen phrase was clearly set forth by the man, John Jay, who asked for its inclusion in the Constitution for the purpose of excluding foreigners from the office. His intent was to exclude foreigners and their children from the office, and the House of Commons, Vattel’s Law of Nations, and the droit d’abain of France all clearly indicate the children of aliens used in the international context were to be excluded to protect the Republic.