@MikeMason-- Doesn't this syndrome usually result from a tumor in the endocrine system?
I think an abnormal growth in one of the endocrine organs causes endocrine cells in the digestive system to produce more acid.
This actually shows how interlinked the endocrine digestive systems are. In Zollinger-Ellison syndrome, the symptoms are seen in the digestive system, but the cause is actually found in the endocrine system. So treatment has to be directed at the endocrine system which would be the removal of the tumor.