Are Hospital ultrasounds really inaccurate?

My son is rather big and I had gotten an ultrasound at the hospital on 4/10/16 and they measured him up to 30 weeks and 5 days. But my ob/gyn says they won't change my due date because the hospital measurements are inaccurate. So the want to go by my LMP due date (6/25/16) not the hospital ultrasound (6/14/2016).