Well, yes, actually it does. "These are the natives, or natural-born citizens, as distinguihsed from aliens or foreigners." Had this been inserted one sentence later, the meaning would mean what you think it means. Instead, it said that some authorities go further in delcaring persons to be citizens, but it never characterizes nor suggests that such persons can be characterized as natural-born citizens. Instead it says, that such persons' citizenship would be in doubt. IOW, in this context, natural-born means citizenship that is without doubt.
There is absolutely no doubt about the citizenship of a Natural Born Citizen precisely because a Natural Born Citizen is the kind of citizen that cannot be any other kind, naturally. Born on US soil to US citizen parents. Seems pretty plain.