Actually, ducks don't lay down any more than people do. They lay eggs. The way it works is "People lie, ducks lay." Or, as I learned it, chickens.
Update: It has been pointed out to me that Ducks line their nests with their down and thus,in construction terms, do lay down. A new meaning to "comfy layers of down".
The most famous person to ignore both ducks and chickens is probably Bob Dylan in "Lay, Lady, Lay" who isn't, in the song, doing it in the Gritchkaian sense, and has confused a generation.