Barkly,
I'm a radio engineer by profession (thus the title) - and have been for over 40 years. I've also been involved in the production of EMC (Electro Magnetic Compatibility) standards for radio comms equipment, and I am chairman of an international standards committee on certain types of radio. So I claim a certain amount of professional knowledge, and I will say that MP3 players (amongst other things) can radiate on all sorts of frequencies.
It's interesting that they never call for hearing aids to be switched off, though, and some of the more modern ones of those use radio. Admittedly the power level is so low and the frequencies so well defined that I have an email from the CAA on file in which they say they're OK.