one further point....you are getting hung up on the word national. They are using it to mean citizen. You can see this on US State Dept websites and well as in the seminal US Supreme Court decision listed on my profile that discusses this very law.
The law makes a clear distinction between the two. All citizens are nationals, but not all nationals are citizens.
After looking at the State FAM, I'll concede that they are enforcing it as if it "nationality status" meant "citizen" or Non citizen national. Thus if the unwed mother is a non citizen national, the baby born outside the US is non-citizen national, if she's a citizen he's a citizen. But in either case, by law, not necessarily natural born per the Constitution. The FAM says that too.