LOL, then why does a person only have to live in the U.S. for 14 years to be President? The requirements are not as strict as you would like to argue. Certainly the founders intent would never have been to rule out a baby born in another country to a citizen who then came here and lived the rest of his life here. That would be an absurd original intent. That’s why they used the phrase natural-born. In Britain, that phrase covered children born outside of the country to citizens.
They certainly are, notice that even the contingency of someone born here to citizen parents was not enough for the Founders. They put in an additional requirement to disqualify a child born here and taken abroad unless they had returned for a substantial period of time.
I do not find that the British historic law is as you have stated. Clearly to be natural born required the parents (father) to have been under the allegiance of the king.
"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."