I had a couple of new Hearthstone players over. The three of us (2 on Android, one on PC) signed in, and the PC player and I played some challenge matches. After a few games, the PC player got the Fireside Friends achievement. I did not. I checked to verify that I didn't already have the card back. He hadn't played at all prior to this event. Why might I not have gotten the achievement when he did?
Make sure you played at least 3 games against a player on the same subnet with at least 3 of you logged into Hearthstone on the same subnet.
You may have to sign out of Battle.net and sign back in. I know that some people said that swapping the device they play on worked out too. Try logging onto your friends PC and having 3 games on your account to see if it unlocks.