Okay. Here's where we're tripping up.
You have obviously decided to take the position that if the law doesn't EXPLICITLY say, "Persons born overseas to US citizen parents are to be considered NATURAL BORN citizens," then it can't mean that they are natural born citizens.
In other words, I am assuming that you accept that the Framers of the Constitution intended that Congress had the ability to say who, born abroad, was and was not a natural born citizen.
You simply maintain that unless they include the words "natural born" in the law, and spell it out specifically, such persons aren't to be considered natural born citizens.
Am I correct here?
Assuming that I am: I can understand such a viewpoint.
The problem is that whatever the 3rd Congress intended in dropping the words "natural born" from the 1795 Naturalization Act, succeeding Congresses have passed succeeding acts. The 1795 Act went out of force a couple hundred years ago.
So in order to understand what the law currently means, we would need to consider the intent of the Congress or Congresses that passed the laws now in force.
The pretty much universal understanding since then, of our courts, our legislatures, and the general public, has been that if someone is born a citizen, that person is a natural born citizen.
In other words, whatever the 1795 Congress intended, succeeding Congresses intended for US citizens born to citizen parents abroad to be equal to those born US citizens here.
This understanding was strong enough, and pervasive enough, for James Bayard to write in 1834 that being a natural born citizen only required citizenship by birth, and that those born overseas to US citizen parents were eligible to be President - and for Chief Justice Marshall to agree.
So why didn't succeeding Congresses include the magic words "natural born?" They simply didn't think it was necessary. Either that, or they simply didn't consider whether any of these citizens might want to run for President and "need" those words.
Because everyone pretty much understood that if you were born a citizen, then you were a natural born citizen and eligible to run for President.
That's my understanding.
And you may disagree. If so, then we'll just have to agree to disagree.
But based on the evidence from Bayard and Marshall, and so many other things, I'm confident that understanding is the correct one.
The law says what it says. You can not read in what is not there nor read out what is there.