Due date changed by early scan, doc didn't update?

Hilary
My LMP due date is 12/20. But my dating scan taken at 7w and again at 9w both said I'm due 12/16. So I've been thinking since then that's my due date. 
Yesterday was my first apt at high risk doc, and they're using the LMP date. When I asked why nurse said it's just what the original doc sent. I told her of dating scan and she said it probably won't change my official due date since the dates are so close together. 
Umm.. But 4 days IS awhile when it comes to overdue babies! Am I wrong to want them to change it to the 12/16 date?