Chris- I think your fact checker may be a bit out of calibration. Very few got anything from the factory even the Sox & Martins of the world and if they did it was seconds and the teams were thankful for it! The car clinics that the factories put together were for the benefit of the car buying public more so than that of the race car teams. I've heard the color white story a zillon times, I don't know who started that one but 95% of those cars took a bath in acid before any construction began so color was irrelevant.
Sounds like a bit of confusion - "Body- in- white" is a term that has nothing to do with color- it's a term referring to an assembled car body bare, without mechanical parts or trim (or even a VIN), not a "white car body".
Don't know how these would have been shipped, either bare metal or the dip tank primer seem most likely
As mentioned most of the race cars were acid dipped and given additional tweaks- Chrysler didn't build the cars, the big racers generally had good sized shops of their own and a stripped unibody was the easiest start for cars. Obviously you had to have a "Direct Connection" to buy a "body in white"- not something the factory was wanting to sell regularly to the general public. A "Factory" team would still have to buy their own parts but have better access to them then the average customer. Being able to buy a stripped body rather than a complete new car still offered a substantial savings to a racer wanting to run a current model "stock appearing" race car
Still haven't figured out how the "exact" shade of pink/orange/red could possibly be important enough to generate so much excitement