“Congress has only power over naturalization. Cruz is a citizen via Congressional action. Ergo, Cruz was naturalized at birth.”
Your statement could only be true if the first act of naturalization in 1790 was unconstitutional. Not one founder ever uttered a single word to indicate in the slightest that anything about this act was amiss. Nothing. Nada. Zilch.
So the founders did not hold your opinion. Even if you are right, and they misunderstood the meaning of their own words, I will gladly be wrong in their company.
The Naturalization Act of 1790 was amended, with the particular offending sentence removed and replaced. I'll also add the words of constitutional scholar Professor Natelson, cited 17 times by the Supreme Court when making their decisions:
Although Congress cannot alter the meaning of a constitutional provision, one may contend that this statute sheds light on the meaning of the constitutional meaning of "natural born." It was adopted by a Congress that included important Founders and it was enacted before all of the 13 original states had ratified the Constitution. But at least four factors weaken its persuasive force: First, the new federal Congress adopted it nearly a year after the Constitution had been ratified by eleven states. Its terms seem not to have been the subject of discussion during the ratification process. Second, the statute is ambiguous. It applies to the “children of citizens.†That may mean children with at least one citizen-parent. But it also might mean children with two citizen-parents. As noted above, other founding era sources that, at first glance, might seem to mean the former, actually mean the latter.
Third, when Congress used the term “citizen†it may well have meant only male citizens. Taken alone, it would not seem so. But remember that the then-prevailing assumption was that citizenship status followed the father. Observe how the statute's proviso focused solely on the father: "[T]he right of citizenship shall not descend to persons whose fathers have never been resident in the United States." Fourth, the presence of "natural born" language in a statute dealing with naturalization and not otherwise with natural born status seems to demand explanation, and one likely explanation may not be good for Senator Cruz's case: During the founding era, certain private rights, such as inheritance and land ownership, could depend on citizenship or natural-born status. Congress may have been seeking, not to explain or define the constitutional requirement, but merely to extend private benefits to persons who might otherwise be excluded. This would explain why the statute provides that the "children . . . shall be considered as natural born" not that they literally are natural born.