Haven't watched the movie, but it came out in 2011, so it's probably relevant: with wifi specifically, it was possible to stop a connection of a device by pretending to be that device and asking the router to stop the connection. Even on an encrypted wifi network, the 'goodbye' signal was not secured. So a jammer device could just spam 'goodbye' to the router, pretending to be everybody else who is trying to broadcast. The router would then stop the connection, and it would take a while for the true device to figure out that it was no longer being listened to.
I assume this no longer works on modern devices, but perhaps it does.