The story about the Mexico-USA war and gringo created as a term to address American people is something they would like to be true in both countries. The fact is that the word is probably a vulgar term for "greek" meaning "a language you can't understand, both written or spoken", later applied to people that spoke such languages. This term is included in the "Diccionario castellano con las voces de ciencias y artes" compiled by Father Esteban de Terrero y Pando and printed in 1790.
If you visit
CORDE, the site of Real Academia Española which database contains selected texts in Spanish from 980 to 1970, you'll find that "gringo" is used in "El Matadero" by Esteban Echeverría, an Argentinian writer, in 1838, and also used by Manuel Bretón de los Herreros, a Spanish writer, in "El Pelo de la Dehesa", published in 1840. In the case of all Argentinian writers of that time, "gringo" means those people who speak Spanish with a strong accent, mainly English, Irish, French and Scotts by that time (including my great great great grandfather ). Echeverría wrote "gringos y herejotes", both derogative and tender terms (herejotes -kind of heretics- because some gringos were Protestant), quite a contradiction, meaning "those who are not alike us". Bretón de los Herreros used gringo to refer to an unintelligible foreign language.
Today the use of the term "gringo" varies from one country to another. In Mexico refers mainly to white Americans, in Argentina and Uruguay means mainly white people of European ancestry, Christian, that don't match the Spanish Mediterranean prototype (what includes me, as I can be described as gringo though now and then they call me "negro" or "negrito" -black or blackie). The term identifies the Germanic type in many countries, because they were British who were wandering by the Americas in the days this word became common lexicon.