AirPods Pro (earbuds) SN does not match case SN

In the discussion for where to locate the AirPods (AP) serial number (SN), #2 states each AP has a SN but does not specifically state if the AP SN is supposed to match the primary SN on the case lid. In the final statement it eludes to the SN might be different than the case base not directly the fact. I was denied the ability to return my AP for replacement because my AP SN does not match the lid and the receipt.

Are the individual SN’s on each AirPod bud supposed to match that of the lid/box?

I purchased these at a non-apple store because i was traveling and there was no apple store within an acceptable distance from where i was for training.