Quite a few people on babybmw have ordered and aren't getting their cars until Feb or March and they are still being given the APR as it is now. When I ordered the dealer told me that if they got the paperwork signed before end of quarter I would be in that deal no matter when the car came. If i were you i'd try to speak to someone more senior. Saying you'll get charged whatever the lowest APR is on the day of delivery is total cock. How can anyone enter into a financial agreement under those circumstances?
Regarding the finance on the new BMW site. It's useful but it's a rough guide based on what BMW finance give the dealers. Individual dealers can give whatever discount or contribution they can afford or want to give. I think APR and minimum deposits are the only things set by BMW finance which is a separate company from BMW. Dealers cannot change the APR. I dare say I'm teaching my granny to suck eggs with this info.