Recent TV specials on the underground railroad and on Harriet Tubman said the song originated during the time of the underground railroad, as I recall sometime in the 1850's. There were several other "spirituals" which also were used for instruction or to tell when the railroad was making its next move.

Re: Paul Campbell - the Weavers used this nom de plume (or more likely, nom de guerre) when they were blacklisted during the McCarthy era.