“... thus, a natural-born citizen is someone that is a citizen at birth, while a naturalized citizen becomes a citizen later in life.” By mistating your premise to include that which you wish to establish as singular truth, you have deceived readers and yourself. Naturalized is a process reached through statute, ie, some legal statute establishes citizenship. By statute is not a state achieved by meeting the primary definition of natural born. Even you can think up a case where someone born on American soil but not a natural born citizen at birth and not a citizen at birth can become a citizen by statute passed later in life yet reaching back to date of birth, state of parents’ citizenship, and location. [HINT: think children born to diplomats and years later Congress establishes a statute covering siad child born to a diplomat of a foreign country.]
A child of foreign diplomats born in the U.S. is not a U.S. citizen because U.S. laws (and, less relevantly, the 14th Amendment) in existence well before 1961 and still in effect today specifically state that the children of foreign diplomats do not acquire U.S. citizenship merely by being born in the U.S. However, the laws of the U.S. in 1961 said that the child of a U.S. citizen and a foreigner is a U.S. citizen at birth if he was born in the U.S. Ergo, if Obama was born in Hawaii, he was a U.S. citizen at birth; if he was born abroad, then he wasn’t (because his citizen mother hadn’t lived in the U.S. for 5 at least years past the age of 14 as the statute required in cases of foreign birth).
Your theory is that a person can be a U.S. citizen at birth and not be a natural-born citizen. I disagree with you, as did, apparently, Joseph Story. That doesn’t prove that you are wrong, but at the very least you should accept that that passage from Story’s Commentaries is a point in my favor.
Well, several classes of people, those born abroad to two citizen parents, and those born to a single citizen parent and an alien father, with some residency restrictions for the citizen parent(s), are also citizens at birth, but via statute. See 8 USC 1401. BTW, the statues themselves define "naturalization" as a acquisition of citizenship *after* birth. See 8 USC 1101, definitions
Of course that position is not logical. The Congress is only granted power to define a uniform rule of naturalization, yet they have defined several cases of "citizenship at birth". But it is Congress, so a little illogic is to be expected.