Not trading for Dejounte Murray: Good call
According to Edwards, Atlanta was looking for one of Ivey or Thompson plus additional assets for Murray and the Pistons turned them down.
Murray is a very good player, a two-way guard who can fill a stat sheet, but the Pistons already have plenty of talent at guard, they need wings, forwards and better role players, not star guards.
Giving up their only real wing player (Thompson) wouldn't help this deficiency and there is a solid chance that Ivey will eventually be as good (or at least close) to Murray and he is much cheaper.
Ivey also has ties to Detroit and wants to be here. Murray may not share those sentiments, so this goes back to the first call: The Pistons can't move any of the Core Four unless they are getting back a proven wing/forward.