The griego etymology sounds suspicious to me. Griego still means Greek. Why would anyone substitute gringo for the same meaning? That would be equivalent to English-speakers saying "it's Grink to me." Griego already had the desired connotation. It doesn't become more international or more derogative when you add the nasal. And it's not shorter, as when norteños say "spic" instead of Hispanic or "aussie" instead of Australian, nor a corruption of an unfamiliar foreign word, as when they say "dago" in place of Diego or "russkie" in place of Русский (rooskiy). Or when the residents of St Joseph, Missouri pronounce the name of founder Joseph Robideaux as "roobidoo."

The lilac etymology is at least plausible. Changing "green grow" to gringo is similar to the corruptions of foreign terms mentioned above. And remember that if you roll your R's, gringo is quite a bit easier to say than "green grow." Moreover, the song appears to have xenophobic and jingoistic sentiment (in the line "change the green lilacs to the red, white, and blue"), which might have made it a symbol of everything one resents about a people who've stolen half of one's country.