In the movie The Outfit, we're told that in that era, the FBI are the only ones with access to tapes and players. If Leonard took one tape and put it in that communication box, wouldn't the FBI have found the player empty when they came to replace the tape?
If the FBI never replaced the tape, how is there another tape recording the events of the day that we are shown in the end? Even the gangsters are shown to have trouble getting access to players and tapes.