It is possible Barbara, I actually thought of that, which would be a hoot in itself!
The date I have for Paint Your Wagon is 1951.
A friend is considering recording this and I was trying to get the background information for him, otherwise I would not be quite as obsessive.
Musically it sounded very similar to me, to some Middle European Folksongs, such as the Hungarian song "Anna Thea (Lazlo Faire)" so initially I wasn't suprised to see a reference to the possibility that it was based on a folksong, but maybe the middle European roots are Lerner and Loewe's.