Some have made that argument, and it is not entirely without validity.
However, it is clear that the Framers who took their seats in the original First Congress, together with President George Washington, both specified quite clearly that such children should be "considered as natural born citizens" (meaning, obviously, that they would be equally eligible to be elected President on meeting the other qualifications to the office), and believed that Congress's Constitutional power to establish a "uniform Rule of Naturalization" extended to declaring that such children could be natural born citizens eligible to be President.
It is also clear that James Bayard, writing in 1833, stated with absolute clarity that birth on US soil was not necessary for Presidential eligibility; that being born a citizen was enough.
It is also clear that Bayard's exposition of the Constitution was reviewed by Chief Justice John Marshall, Supreme Court Justice Joseph Story, Chancellor James Kent and other distinguished legal experts of the early United States, and no one found any fault with his interpretation of "natural born citizen."
Bayard also had another line into the thoughts of the Founders and Framers: His maternal grandfather was Richard Bassett, one of the Signers of the Constitution, who was also the most senior member of the First Congress. He was given the ranks of "Senator #1" of the United States.
It is also clear that no significant legal authority in history has ever drawn any real distinction between "citizen at birth" and "natural born citizen."
Some years ago, a legal scholar named Jill Pryor wrote an article in which she characterized such children as "naturalized-born."
After all the talk on the subject, I find that characterization to be reasonable enough.
Having studied the roots of the entire phrase quite extensively now, I find the dissent in Wong to be generally out of touch with many of the historical meanings and principles. But there is at least one point on which I agree with Chief Justice Fuller's dissent.
Fuller said it was unreasonable to think that the children born on US soil of Mongolian parents were eligible to the Presidency, and the children born abroad to US citizens were not. I agree.
All of this has a very simple and obvious answer. Wong Kim Ark was a US citizen by birth, a natural born citizen and eligible to the Presidency.
Ted Cruz is a US citizen by birth, therefore a natural born citizen and eligible to the Presidency.
It matters not that Wong's natural born citizen status came a bit more directly, via the common law and perhaps the 14th Amendment, and that Cruz's natural born citizen status came through the Constitutional authority of Congress to define, at their discretion, which persons born abroad would also be citizens by birth, natural born citizens.
The Constitution, in effect, has authorized both routes.
And how do I know that the Constitution has authorized both routes - the common law and the discretion of Congress through its power to define a uniform rule of naturalization?
I know it because the men who Signed that Constitution clearly believed that was what the document meant.
If they had not believed that, then they (with President Washington) would never have specified, during the course of the First Congress, that the children born overseas to US citizens were themselves "to be considered as natural-born Citizens."
That's my 2c.
It is also clear that Bayard is contradicted by law.
Ted Cruz is a US citizen by birth, therefore a natural born citizen and eligible to the Presidency.
Ted Cruz is a US citizen by law. The law states that he is a "citizen".