DNS is related to BGP only that without the right BGP routes in the routers, no packets can get to the facebook networks and thus the facbook DNS servers.
That their DNS servers were taken out was a side affect of the root issue - they withdrew all the routes to their networks from the rest of the Internet.
Not picking on you - but there has been a lot of confusion around DNS that is mostly a red herring and people should just drop it from the conversation. Everything on facebook networks disappeared, not just DNS. The main issue is they effectively took a pair of scissors to every one of their internet connections - d'oh!