Except that the Supreme Court says otherwise; that natural-born citizens are only those persons born in the country to citizen parents. Yes, some people are ignorant of the rulings that say this, but the precedent would certainly stand up to specific scrutiny.
There are ONLY 2 types of citizens, Natural born and Naturalized.
Well, no this is false. There are persons who can be citizens at birth who are NOT natural-born citizens. These are persons born under U.S. Code that fit a variety of circumstances. Born anywhere to an unwed mother; born with residency requirements, etc. All you're doing is trying to stretch natural-born citizen to mean something much broader than it actually means. If you have to consider different circumstances such as residency or whether a mother is wed, if the parents were here legally, etc., then you've taken this type of birth citizenship out of the realm of being "natural."
Oh, and where do they say this? Because it sure isn't in Minor v Happersett where they say there is doubt and this case won't resolve that doubt.