Same situation here, 07/2004 E53 3.0d. Got the "oil abrasion" error with INPA, went to dealership, gave the VIN number and they provided the 83220397244 oil, same bottle and E53MU spec, just like in the photo above. They clearly mentioned that my X has no xdrive, while the 83220397244 seems to be intended for xdrive transfer cases. I guess the guy at the desk only counted xdrive vehicles starting with the new xdrive badges.

However, weird thing is that I was unable to reset the "oil abrasion" error even after I replaced the transfer case oil.