IMO there is no reason why serial numbers should match in this case the S/N of the shells.
S/N serve the purpose of identifying and tracking a piece. The PCB S/N is for the hardware, so that if the system need to be serviced, you have a reference for various models to know the hardware variations.
The shell S/N is for commercial purpose and is to keep track of a finished product.
It would have been tedious at the time to make both S/N match as it would require to note and transmit every S/N from the factory where the boards were finalized to where the boards would be placed in the shells.
This mean that if a batch of PCB was discarded due to a manufacture issue, lot of damaged chip, etc... You'd have to wipe out the corresponding shells (especially if the S/N is engraved in them or printed on the shell rather than affixed on a sticker).
Applying S/N per shell is more streamlined and require no care about the PCB numbers.
I'm sure that high end product receive more care, and computerization today would allow to do this for any product, but I doubt that such meticulous care was given for such a product. Not that I suggest that the RCA Studio II is a cheap product, but matching S/N everywhere is a frivolity that you can do only on very high end products.
Hadn't thought of it that way - makes perfect sense. The boards up to at least ±65,000 had handwritten SNs, but at some point, they switched to stickers on the PCB as well, which would have made it easier to align. Sadly, these came off easily - so did the stickers on the shells.
There's also a color change in the PCBs along the way: early models are olive green. At some point, they became something between blue and green. And the auction shows a 'proper' green one.