If I understand your argument correctly, you think there are only two types of citizens: naturalized and natural-born.
US government (INS) published the following document: http://www.uscis.gov/ilink/docView/SLB/HTML/SLB/0-0-0-1/0-0-0-45077/0-0-0-48575.html
This document makes a distinction between a native-born and a natural-born citizen (in three places):
1) “The repatriation provisions of these two most recent enactments also apply to a native- and natural-born citizen woman who expatriated herself by marriage to an alien racially ineligible to citizenship, a category of expatriate not covered by the earlier 1936 legislation...”
2) “The words “shall be deemed to be a citizen of the United States to the same extent as though her marriage to said alien had taken place on or after September 22, 1922”, as they appeared in the 1936 and 1940 statutes, are prospective and restore the status of native-born or natural-born citizen (whichever existed prior to the loss) as of the date citizenship was reacquired....”
3) “The effect of naturalization under the above statutes was not to erase the previous period of alienage, but to restore the person to the status if naturalized, native, or natural-born citizen, as determined by her status prior to loss. “
And where is native born mentioned in the Constitution?