there was a mythbusters on this. if i recall correctly, though they couldn't find any way to make the plane's instrumentation fail by bombarding it with a myriad of frequencies, even the mythbusters guys (possibly for legal reasons, or because they succumbed to pressure from their network) concluded that because the FAA can't rigorously test every device that comes out, that this is somewhat of a blanket policy to ensure that some new device that nobody has tested will be on during takeoff and cause the plane to crash.
this said, i never power off my devices...just put them in airplane mode if they have them, or to sleep. i fly a lot, both domestically and internationally.
If you broadcast on the radio frequency the pilot is speaking on, you can jam their transmission.
If you broadcast on, say, the instrument landing frequency (ILS) frequency, the ILS needle the pilot is looking at will stay centered, no matter how much he deviates from the approach path.
The pilot would undoubtedly realize something was amiss, switch comm frequencies, use GPS etc. But it could cause some distraction and wreak some havoc.
Back in the 90s, there were cheap CD players and whatnot that would generate all kinds of crazy RF.
The FAA said, this is all unapproved electronics, we can't test it, it has to go off during takeoff and landing, unless the pilot OKs it. Of course, the corporate pilot will OK it for his CEO/passenger.
this said, i never power off my devices...just put them in airplane mode if they have them, or to sleep. i fly a lot, both domestically and internationally.