It appears it's to do with country of residence rather than country of birth.....
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1130.html#entry_requirements
....Children under 18 years of age who reside in Argentina, regardless of nationality, are required to present a notarized document that certifies both parents' permission for the child's departure from Argentina when the child is traveling alone, with only one parent, or in someone else's custody.
http://travel.state.gov/travel/cis_pa_tw/cis/cis_1130.html#entry_requirements
....Children under 18 years of age who reside in Argentina, regardless of nationality, are required to present a notarized document that certifies both parents' permission for the child's departure from Argentina when the child is traveling alone, with only one parent, or in someone else's custody.