If the device had a long time delay or a delay based on the number of flights they might have to check many flights before the affected flight. And there is no guarantee the person would use the same delay each time.
If they pick flights on routes that have a lot of repeat travelers and the delays on the device make it so the airline has to look at a fews days worth of flights to get the suspects for each incidents then I'd not be surprised if there are may people that were on all the planes sometime before the affected flights.
The big problem I see with it being done by someone not on the flight is that surely after the first couple of times the PA system is going to get thoroughly inspected and the device would be found. The mystery would then just be "who", rather than the "how" mystery that we currently (at least publicly) have.