Maybe it would be better if Gene said BMI and ASCAP show "who claim it." In this case, it's the Weavers and Paul Clayton. the Weavers resurrected a lot of traditional songs; but this one sounds like it was composed, and not subjected to the Folk Process.From what I can see in a review of recordings of the song, it seems it's generally credited to Paul Clayton, a gifted folk musician who died too young.
If you do a SuperSearch of Mudcat, you'll find we've had some interesting discussions of Clayton, and some comments from Mudcatters who knew him.
-Joe Offer-