Your post is about what the law should be, not what it is.
The Supremes have never ruled precisely on the "natural-born" issue, but it really isn't difficult to examine the rulings they have made and deduce how they likely would rule. Which would be that natural-born is the same as native-born, leaving us with two categories of citizenship, not three.
The Constitution itself mentions three (3) so are you saying that it doesn’t? Do you defy the words printed in black in white that are before you? Let me spell them out for you:
1. Citizen
2. Naturalized Citizen
3. Natural Born Citizen
Only one of the above applies to the offices of President and Vice President. In case you still don’t get it, that would be #3. That’s what is being discussed here, not citizenship rights, and definitely not British Common Law, which we Americans detest to this day.