Of course they do. And they watch Match of the Day. On a Monday or Tuesday, when the elite panel of referees gather for a review of the past week's games, there's time for informal chatter amongst the refs and you can bet your bottom dollar they gossip about players, especially those who are the worst behaved.
And that's why Luis Suarez is going to have to virtually lose a leg if he wants to get a penalty in English football. refs remember, especially when they're made to look stupid by some crafty player like Suarez, who has almost made an art form out of sneaky handballs and dives.
Today, as Liverpool and Villa struggled for supremacy, Suarez claimed two penalties and there was indeed some slight contact on both occasions. But there wasn't enough contact to go down either time and there's no way a Premier League referee is going to give him a penalty unless the foul is obvious for the world to see.
In fact, it does seem to me that referees have made a subtle shift away from those claiming penalties and are becoming more prepared to hand out yellow cards for simulation.
They'll get these wrong sometimes, but I'm afraid it's more than worth a few harsh bookings if it means that it begins the process of stamping out diving.