Budd themselves were said to have preferred the cars unpainted.
Not sure what kind of business would allow their vendors to dictate their branding for them. (Pullman got away with putting "Pullman" on the sides of their cars because they owned them.) I highly doubt many railroads paid much attention to Budd's wishes after buying their cars unless it saved them .
Actually, as a result of an antitrust action in the mid-1940's there are two companies involved:
Pullman-Standard - the manufacturer,
The Pullman Company - the operating company.
The operating company was sold to a consortium of 57 railroads which actually owned the cars and leased them to Pullman to staff and operate them. That is why the Pullman name appeared on those cars (regardless of the builder)- generallly with the owning railroads name in small letters near the door. The operating company ceased operation at the end of 1968 and the few remaning sleepers were operated by the owning carriers untll Amtrak in 1971.
And this brings us to why sleeping cars used to be called "pullmans". That referencing the operating company rather than the Pullman-Standard manufacturing company. We are indeed speaking of sleeping cars built by any and all manufacturers.
Not every railroad participated with the Pullman Company,but the vast majority did.
So what was the point of the Pullman Company? It meant cars could be shuttled around all over the nation as needed with a minimum of trouble. Of course we do not need a special company to do that today since Amtrak is all one national company.
But look back to the days when there were about 100 railroads with passenger services. They needed all the cooperation they could use back then. Keep in mind that some railroads were in competiton with each other--something we can scarcely imagine today with one national company always fighting for its one budget.
The pullman company enabled cars to be shuffled around in many different ways as needed. For example a point frequently mentioned here is how extra pullmans were put on the Florida trains during the winter. Well, some of these were borrowed from Western railroads which were not as busy in the winter. The Florida Special, the South Wind, the City of Miami and others often had "foreign lines" on them--like Great Northern,Northern Pacific, Union Pacific and others. And of course special moves, like political conventions, football games, the Kentuky Derby,etc, needed all the help they could get from the Pullman company.
Again, the whole concept is completely useless today since we have just one national company to shuffle its equipment around as needed (if we have it, that is)without any permission from any alien body.
If a pullman car was bad ordered and there was no spare from the operating railroad, then, thanks, to the pullman company, sometimes a car could be borrowed from an off-line railroad should it happen to be available.
Keep in mind that there were literally dozens of sleeping car/pullman configurations back then. By no means was it just 10-6's. So, if a train's pullman with l2 bedrooms was on the blink, and the only spare had 22 roomettes, they had a problem. But what if another railroad cooperating with Pullman had a 12 bedroom it would not need for awhile, then perhaps that could be temporarily borrowed.
It was interesting, as a child, to see the trains come in sometimes with some kind of oddball cars from a strange railroad. Of course we get some of that today,like when the Vermonter baggage car was going all around the country not too long ago.