I hear this claim a lot and it always sounds simplistic. The most reliable refutation a quick google turned up was:
http://www.mayoclinic.com/health/digestion/AN01776/
from a gastroenterologist at the Mayo Clinic. I quote:
"There's no concern that water will dilute the digestive juices or interfere with digestion. In fact, drinking water during or after a meal can actually improve digestion. Water and other liquids help break down the food in your stomach and keep your digestive system on track."
Food stays in your stomach as long as 5 hours. Water must get absorbed/passed on much more quickly. (I couldn't find numbers.) I imagine your stomach is pretty smart about maintaining a proper environment for digestion.