Go to the image pages and look at the stones in gallbladders sugically removed. Look familiar?
The bile released from the liver digests fat. The large amount of oil ingested all at once sends a signal to the liver to release bile with great force. This force also pushes out stones in the ducts. Sometimes there is a little oil discharged in the bowel, but most of it is broken up and digested just like any other fat you consume.