The concern was intermodulation, which can occur when two signals of different frequencies are combined in a circuit that is not completely linear, I.e. has some distortion. This causes new frequencies to be generated which could interfere with communication or navigation. Experience and testing apparently showed that it was not a problem.
With dozens of people using phones, mp3 players and other devices during take off and landings (most people just say OK when asked to turn them off, wait for the attendant to move on and then go straight back to doing what they were doing) this all seems like a silly argument as they has been no evidence at all of anything actually effecting anything to do with the control of the aircraft.