Some people through no actions of their own were born in a foreign country.
Of course. But the Constitution makes no mention of the issue of dual citizenship. The only issue is whether one is a natural-born citizen or a naturalized citizen. Those are the only two categories of citizen. If you do not fall into one category, then you must fall into the other.
It isn't necessarily either or.
Even is something as fundamental as sex, one could assume that anyone who is not female must be male. Yet there are people born every day with both or neither sets of reproductive plumbing.
OK. Go with DNA? XY=male. XX=female.
As the Olympics have shown, some fully female women from birth are genetically male.
And what about XXY individuals? 2/3rds male, 2/3rds female?