Some birther's argue that "natural born citizen" and "native born citizen" are not the same, now you present evidence that indicate they are.
Some birthers claim that citizenship naturally follows that of the father, passed on in the sperm, if you will - do you offer the above quote as evidence that the baby inherits citizenship from both the egg and the sperm?
The quote does not say "both parents" nor does it say "parents, one of which is a citizen", it is simply plural as "citizens" and "natives" are plural. We might assume that because natives and citizens are a broad class of people, more than one set of parents gave life to them, and that among those pairs of parents were some of mixed citizenship.
The term "native-born" -- I don't know.
With regard to your other question, until the Cable Act of 1922, and citizenship laws of the 1930s a woman who married a man acquired his citizenship status upon marriage, not vice versa. So yes, the citizenship of the father was automatically the citizenship of the child. The citizenship of the mother was almost irrelevant because that citizenship followed that of her husband as well.
So it doesn't have to explicitly say "both parents". Anyone familiar with the law throughout American history would know that the father's citizenship was all that was important, because it was not possible for the mother to have a citizenship different from her husband.
Anchor baby's are native born by statue (i.e. not naturally, but because some legislatures decided that was a good idea at the time).
An anchor baby can actually have triple citizenship at birth. US citizenship by being born in country, foreign citizenship from country B inherited from the father and foreign citizenship from country C inherited from the mother. Furthermore, the child will not only have been born to foreigners, but to at least one foreigner who broke our immigration laws on top of it.
Barry was born a subject of the crown of her Majesty the Queen of England.