I had the OEM adapter removed from my brand new X3 2 weeks ago. BMW actually gave me a partial refund. I have 4 and 5G iPods and both worked OK.
My problem was that the adapter only supports 99 tracks in each of those 5 "BMW" playlists. When it finishes track 99 it goes back to track 1. This meant I could only access about 495 songs out of the 5000 on my iPod.
I would check it if I was you.
I have since bought and installed a Dice Silverline. It too has plenty of problems but at least it can access all my music.
Funny they ordered the wrong part for you. I had the same thing happen - resulted in a 2 day delay in the delivery of my new vehicle.
I have the OEM Adapter instructions here still. I have attached a picture of the compatability page for you. It says G3 are supported from firmware 2.3 up.