Why is it recommended to wait 20-30 minutes to eat after a work out?

I haven't heard that before. Probably like ray said to let your stomach and body settle. I know before you work out you need to give yourself some time between eating and working out. But after a workout I've always been told to try and eat or drink some protein within 30 minutes.

Digestion does reduce the amount of blood circulating to the muscles to some degree, because additional circulation is needed to aid the digestive process. With a reduction in the amount of blood—and thus oxygen—muscles receive following a large meal, muscle cramps are more likely during any exercise undertaken soon after.

It is a matter of blood flow the blood that is required for proper digestion is moved to the muscles you have exercised. if you eat right away the food will not be digested as quickly as if you wait before eating.

Your food has to to digest a little bit before you work out or you will be sick.

so you won't get an upset stomach.