Just because FB does not display/store them with your FB conversations, it does not mean that they are not forwarding them to their servers before forwarding them onto your SMS app.But it DOESN'T do that. SMS/MMS is still handled by the stock messaging app, the FB app only acts as a front end display. FB DOES NOT SEE SMS EVEN THOUGH I USE THE APP FOR MESSAGE HANDLING.
How do I know this? Simple. People I SMS with - those conversations appear in my stock messaging app. They DO NOT appear in my FB conversations. Same goes for FB messaging. These only appear in FB messenger and not my SMS app.