There are three types of citizenship
* Natural Born Citizen, two citizen parents born on soil (exceptions for foreign born if parents are abroad in service to country) McCain
* Citizen by birth, foreign born to citizen parent(s) Ted Cruz
* Naturalized citizen, a person made a citizen by statute. Rafael Cruz
I base the above on the following
The authors cite to the Naturalization Act of 1790 and ignore the fact that the Naturalization Act of 1795, with the lead of then-Rep. James Madison and with the approval of President George Washington, repealed it and specifically changed "shall be considered as natural born citizens" to "shall be considered as citizens of the United States."
James Madison the "father of the Constitution" changed the wording from "natural born citizen" to "citizen". Madison was no dope and the change was to prevent a foriegn born from becoming Commander in Chief. But this also serves to illustrate that "citizen at birth" does not mean "natural born citizen".
See more at
https://cdrkerchner.wordpress.com/tag/harvard-law-review/
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Your interpretation is your own, and is found nowhere else, because it is specious.