Absolutely, the direction of influence between the different sources is a minefield. In most cases I would imagine influences were flying back and forth between the different genres at quite a rate. Some channels of influence are more obvious than others.

African-American culture parodied/utilised in minstrel genre.
Land-based work song on water-based worksong.
Once the minstrel craze took off - universal influence.
To mention but a few.