I would have been more inclined to ask where the fisher... uh fisherperon's feet were.
Fly fishing in waders or in a boat, in the river. Sitting idly under a tree with a line in the water, by the river.
But I really wouldn't notice which preposition (of those three) was used. I'd get it. Someone was fishing and it was for fish in a river, not a pond, lake, stream, or ocean.
It just doesn't matter. They get fish from the river. If it were important, the writer would need to say "They fished from their little boat on the river" or "They waded into the river to catch the fish" or "They sat on the bank, talking amiably while their lines bobbed in the water" or whatever was needed to paint the picture.