Love this thread.   It reminds me that language is alive and does not stay static. Example is Shakespearean English or 1700 Revolutionary English and todays American English. Or the term gay meaning happy and today it almost exclusively means homosexual in the younger generation of today   
    I grew up a gringa in a hispanic society, BTW do not call the older generation chicano - it is an insult. At the time I was a kid it was an insult, but I found that if I embraced the term it lost its effectiveness as an insult. Today in the Southwest, it is an acceptable term.   
    After reading all the submissions, I suspect the truth is something like: the term meant foreigner or Greek, then as the Mexicans used it to refer to the Americans during the Mexican war Americans became curious as to what it meant. Not wanting to anger the American facing him, the Mexican related it to a song he had heard and thus the rumor began.
    I have experienced this with curse words in Spanish. When you ask what it means you get a watered down answer. Or for example I thought the word truchas meant danger or scatter or run because we used it to warn the kids the teacher was coming. I was 30 yr old before I found out it meant trout. Thus the scatter.
   Language origins can be so interesting.