fiber doesn't get digested. the keeps things moving comes from the fact that it keeps the digestive system clean buy preventing buildup of food on the intestinal wall keeping that colon healthy.
Maybe this will help with all the conflicting opinions.
Soluble fiber: lower blood cholesterol, slow glucose absorption, slow transit of food through upper digestive tract, softens stools
Insoluble fiber: softens stools, regulat bowel movements, speed transit of material through small intestine, increases strength of digestive system walls