I suspect there is some method to their madness and cars are not parked totally random, but I agree that there is still opportunity for things to go wrong.
Certainly at West Drayton, cars were being bought in from somewhere in Stockley Park (quite a sight actually seeing 5 or 6 silent cars arriving on mass in a row) and the cars that were there were not necessarily just for that day. For instance, 'our' car got lost on route between Southampton and delivery centre. However they were able to fetch 'someone elses' car from Stockley that was due to be delivered a few days later and give us 'theirs' - and they presumably they got 'ours' once it was found - transporter rumoured to have been impounded somewhere in Winchester with no access for a few days. Similar happened to someone else the day before, probably on same transporter, but no immediate spare so he had to come back the next day. We only had to spend most of the day at the delivery centre, but were looked after well until the actual handover.
So they are still juggling VINs right up to moment of delivery, which is why you should not insure you car on the VIN.