Serial numbers that are supposed to be unique aren't necessarily unique. I would guess that the BIOS talk to an EEPROM on the RAM modules rather than to the memory chips themselves. It would be very easy for a manufacturer to flash identical contents to every EEPROM in a batch, or with a sequentially increasing serial, rather than bother with a database.

What if you reinsert the same RAM stick into the same slot? Minute differences in insertion force and direction can lead to the frequency response of the RAM stick changing. Data paths might now be a micrometer long and require the BIOS to retrain the communication controller to compensate for that.

DDR5 tops out somewhere around 8 Gigahertz clock speed, which means the data signals travel 3 centimeters before the next clock signal arrives. At those time scales it means you're going to have to align those data signals down to the micrometer if you want them to be properly received.