A 52-year-old man with a 10-year history of GERD is found to have elevated fasting serum gastrin (240 pg/mL, normal <100) and gastric pH <2 despite omeprazole 40 mg daily. Secretin stimulation test shows a paradoxical rise in serum gastrin. Which feature best distinguishes Zollinger-Ellison syndrome from primary hyperparathyroidism-associated hypercalcaemia in this patient's acid hypersecretion?