No, the chart clearly defines those born overseas as citizens if one of their parents is a citizen.
Naturalization Act of 1790;
"Congress first recognized the citizenship of children born to U.S. parents overseas on March 26, 1790, stating that "the children of citizens of the United States, that may be born beyond sea, or out of the limits of the United States, shall be considered as natural born citizens: Provided, That the right of citizenship shall not descend to persons whose fathers have never been resident in the United States."
Immigration and Nationality Act of 1952
This act exteneded American Citizenship to people born in Guam, Commonwealth of the Northern Mariana Islands, Puerto Rico, Virgin Islands of the United States, American Samoa and Swains Island.