US Immigrations designation "WithOut Papers."

I've read in several places (Urban Legends, and I think alt.English.usage FAQ) that that is a folk etymology. But I don't know what the real one is. The Dictionary of Newfoundland English ( implies that the term referred to university students working WithOut Pay in the 1920s. Since I've read other things that say it's not an acronym, I'm not sure I believe that. Anyone have a better source?