Because walnuts have so much fat and oil in them, they can cause diarrhea if they are consumed in great quantities over a short period of time. The fact is that just about any food with oil in it can cause a person who eats it diarrhea if they have enough of it. Some people are more sensitive to certain foods than others, so it does depend largely on the individual.
Many people are allergic to nuts and therefore have an adverse reaction which can cause problems like diarrhea and in some severe cases problems breathing properly. The fact that walnuts also have a lot of fiber in them can contribute to getting diarrhea after eating enough of them at one time.