Yeah I think this is most likely. Then when you change the serial you're using the calibration data for the wrong screen, but most of the time you're lucky and the two screens behave close enough that an average user doesn't notice.
However, I wonder why the pen calibration data is not stored on an controller on the display panel? That would absolutely make sense.
Pencil also has a small calibration table and when paired with a new iPad it checks and downloads that immediately.
If not, it might also be (more likely) sending whatever it senses to iPad and iPad processes that raw input with the calibration data to determine the final output.