Citizen at birth via statute is not the same thing as natural born citizen.
SEC. 3. And be it further enacted, that the children of persons duly naturalized, dwelling within the United States, and being under the age of twenty-one years, at the time of such naturalization, and the children of citizens of the United States, born out of the limits and jurisdiction of the United States, shall be considered as citizens of the United States:
Provided, That the right of citizenship shall not descend to persons, whose fathers have never been resident of the United States: Provided also, That no person heretofore proscribed by any state, or who has been legally convicted of having joined the army of Great Britain during the late war, shall be admitted a citizen as foresaid, without the consent of the legislature of the state, in which such person was proscribed.
It should be noted that in the rule the residency requirement refers to those who are already citizens...
For example: If I was born in Canada with American citizen parents, I would be a natural born citizen...If I grew up in Canada and married another American citizen but I never resided in the U.S., my offspring would not be American citizens even tho their parents were...
If Cruz's father was a citizen per the citizenship rule, Ted is certainly a natural born American...
Secondly. He shall, at the time of his application to be admitted, declare on oath or affirmation before some one of the courts aforesaid, that he has resided within the United States, five years at least, and within the state or territory, where such court is at the time held, one year at least; that he will support the constitution of the United States; and that he does absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state, or sovereignty whatever, and particularly by name, the prince, potentate, state, or sovereignty, whereof he was before a citizen or subject; which proceedings shall be recorded by the clerk of the court.
Thirdly. The court admitting such alien shall be satisfied that he has resided within the limits and under the jurisdiction of the United States five years; and it shall further appear to their satisfaction, that during that time, he has behaved as a man of a good moral character, attached to the principles of the constitution of the United States, and well disposed to the good order and happiness of the same.