The reason for wanting to construct such a database must mean that BSSID can be retrieved at their (database maintainers, such as Google) end
No. There's more ways to retrieve information about wireless networks. Google drives around taking photos for Street view. I would be surprised if those cars don't log WiFi networks seen as well.
Google also happens to make software for gadgets with a GPS receiver and WiFi Receiver. It seems they use these gadgets, commonly referred to as phones to gather data as well.
You also have crowsourced databases such as Wigle.
and then matched to their saved location. Is that correct? If that is correct, I wonder why BSSID would need to be sent beyond the Access Point?
Applications may send it, but that's data sent by the device, on purpose. It's not included at the network level. If you wonder, fire up a packet logger, such as Wireshark and watch what leaves your computer.