More recently we've taken the approach of "close enough is good enough". See Red Dead Redemptions "hilarious" cut scenes where the NPCs get involved, or the horse grts attached to the trains.

Another thing to consider about a replay system is that you don't have to be perfect. What you as a player see isn't what the server(if you have one) sees, and it's not what the other player sees. Your view is only a best guess at that, and for most replay systems in games, they will also be best guesses.