If someone just starts looking at Facebook during a conversation, think of it like the equivalent of nodding and saying "uh-huh" over and over again -- it's a strategy of ending a conversation. Somebody has to do it, and it's not at the whims of the guy who shuts up last.
So why not do the nodding instead? Surely it's more trouble to whip out the phone and start browsing?
The nodding thing means "yeah we're done" and suddenly browsing Facebook is more like "I don't give a shit, go away", which is definitely more rude.