Then why does Article II, section 1, pa. 5 add an exception to the requirement that the President be a "natural born citizen," so that anyone who was a citizen (of any sort) when the Constitution was adopted was eligible to be President? If "natural born citizen" just means "anyone born in the US," THEN THE EXCEPTION IS TOTALLY UNNECESSARY. Read the entire argument Madison makes in which you found that quote to see beyond doubt that that's true.
No, it is not. If "natural born citizen" means "anyone born in the US," then the exception was TOTALLY NECESSARY, because, in 1789, there was NOT A SINGLE PERSON who was 35 years of age AND had been "born in the US," because the US did not exist 35 years prior to 1789.