I'm brand new to this forum, but thought I should chime in and clear the paint code issue up. I am a spray painter and own a bodyshop.
Firstly, the last 3 digit thing is simply NOT true. Could you imagine that IF the paint code were the last 3 digits how confusing that would be? Every car of the same colour would have the exact same three last digits. They produce thousands of the same cars....it would be impossible to use the same last three numbers for every car of the same colour....they'd run out of VIN numbers very quickly.
The reason why the dealer asked for the last 3 of the VIN is because they enter that into their lookup system and it gives them all the details on the vehicle....model, colour and options etc. This info is contained on a BMW internal information system and is not publicly accessible.