From years of working renaissance faires, doing research, and most importantly being stuck... er... located next to an ocarina booth that only taught its' hawkers to play this one song (out of tune as only clay ocarinas can be)...
I'm firmly convinced that Greensleeves is in fact a corruption of the original Old English, "Graena Slaviis", or "Insane Bastards". This would fit, as the song is currently played at most renfaires the way it was meant to be - over and over again, poorly, and most importantly, off key.
Originally, this song was probably meant as the earliest form known of psychological warfare - played by a horde of drunken, deaf 'musicians', the hope would be that the opposing army would instantly drop their arms, covering their ears and running howling to the nearest tavern to get drunk. Unfortunately, what few historic references there are show that the effect was universal, and the song quickly spread like a virus as the now very drunk ex-soldiers tried to explain why they felt it necessary to drink so heavily.
My opinion, in any case.