It's the BSSID that is made far more readily available, not the SSID.

It's not the SSIDs but the BSSIDs that end up in the database, isn't it?

Yep. These services only store and transmit the BSSID (which is most often the mac address of the network card).

The only place the SSID (clear text name) is used is in filtering out things on the client end. Both looking for "no SSID" / hidden networks and the _nomap suffix. The SSID is never sent to any service.