"The exit of the stomach into the small intestines is on the lower right hand side of the stomach. When you drink, the saltwater goes to the bottom of the stomach, below the opening. To get the saltwater into the small intestine, you need to tip the stomach like a teapot so the saltwater flows out. That's why you lie on your right side."
Errr... I think salt water purging is a good idea to do occasionally to flush out the system but that's plain wrong; the same movement of the muscles of the intestine that propels food/liquid throughout the gut ("peristalsis") works when moving food/liquid between the stomach and the duodenum... There is a sphincter between the two that keeps it shut most of the time until pressure in the stomach is registered by "stretch receptors" which stimulate the contraction of various muscles to open this sphincter and let contents pass.
It's probably a good idea anyway though, just to lie down and relax while it courses through your system.