Correct or not, and I agree that many are not, they are treated as "settling the issue as a matter of law."
If, hypothetically, the case went before SCOTUS, and SCOTUS said Cruz was naturalized, we'd be in the same boat as far as public dialog goes, but a different boat as far as whether Cruz could occupy the office.
Would you LOL if SCOTUS said a citizen born under the law that Cruz was, was a naturalized citizen?
Whatever.
My point is that it would be an incorrect ruling.
A person either earns citizenship, which is "naturalization" or a person has a natural birth right to citizenship, which is being "naturally born".
Any third category of citizenship, such as somebody being "naturalized at birth" (lol) is silly. Logically, how does somebody earn something a birth? You can't earn something without doing something, it just doesn't make sense.