I'm glad to find this resource, which confirms my memory of at least the first two verses of the song. Since we're gathering the folklore around the song, I'll just add my own memories of singing it at local campouts, as well as at Camp Miter Peak, in West Texas, in the late 1960s:

"Barges" was often the last song we'd sing at night, beginning it as we made our way from the campfire to our tents. (Picture all the flashlights moving from the fire through the darkness to the tents -- about as close to "flowing down the river to the sea" that desert-dwelling Scouts would get!) I think the counselors and maybe oldest girls would put out the fire while the younger ones made our way to the tents. I vaguely remember humming the third verse as we stood outside the tents, then we'd sing the first two lines of the verse as a sort of "tag." Then everyone moved inside to get ready to bed down. It wasn't a melancholy song to us, but a peaceful one.

After the counselors called for "lights out" and everyone was (supposedly) all quiet, the tentful of oldest girls would begin this parody, joined by the other campers after the second line:

COUNSELORS
(a parody)

Out of my tent flap, looking in the night,
I can see the couns'lors having a fight.
Silently go the campers to their beds,
But the couns'lors do go noisily.

Couns'lors, I would like to go with you!
I would like to stay up very late too!
Couns'lors, have you candy in your tent?
Do you fight with couns'lors old and bent?

(Repeat verse and chorus)

Out of my tent flap, looking in the night,
I can see the couns'lors having a fight.


After a good laugh, the counselors would bid us good night and do whatever it is that counselors do while campers sleep peacefully -- preparing for the next day's activities, most likely.

I really don't remember hearing a story attached to the song, but we certainly used our imaginations, picturing ourselves living by a river and seeing the barges flowing past with green and red lights. (I'll try to remember the "true" origins from Joe Offer and pass them along!)