A person parks a vehicle and begins canoeing at a point along a stream, B, which is equidistant from two points on the stream, A and C. The stream flows from point C toward point A and beyond.  If the person canoes to point C, “up” stream, and loses all means of locomotion then the person can simply ride the current back to point B.  However, if the person canoes from point B to point A, “down” stream and loses all means of locomotion then the only way to get back to point B is by portaging the canoe.  Therefore, the idiom should be “DOWN shit creek without a paddle.”  QED.