That's why I crossed out the word "not" in your sentence.
I conclude that my old history book was wrong about the "natural born" clause being intended to exclude Hamilton. I have found references to this theory, but a simple reading of the clause itself seems to invalidate it.
On the other hand, I don't see any references to the wording of the clause specifically to include Hamilton.
The "fourteen years" clause does not seem to have been written with Hamilton in mind, although it is an interesting point that he had been a resident for only about 16 years when the clause was adopted.
The "Citizen of the United States, at the time of the Adoption of this Constitution" would certainly "grandfather" him in. But the clause was broad enough to include many other potential candidates as well.
There could be contemporary correspondence that would link either or both of these clauses to Hamilton that I haven't discovered, though.