Corporate rules rarely care about logic.

Tooth filings pick up AM, not FM. Assuming that’s even a real thing. All you need get AM is a diode which can be made to varying levels of performance with a number of common materials.

FM radios generally use superheterodyne receivers which generate a radio frequency to be mixed with the incoming signal to pull out audio.

This receiver does emit a small amount of RF as a result and it’s how the TV police in the UK would catch you for skirting a TV license.

FM receivers are capable of producing interference. Note their listing here.

The weird thing about this post is that both of the obvious scenarios that would lead to the kind of restrictions OP’s workplace has don’t quite add up.

• If radios are banned due to interference, random electronic devices like digital music players are also capable of producing interference. It’s surprising that any kind of personally owned electronic gadget is allowed.
• If it’s a high-security environment, it’s surprising that any personally owned digital storage device is allowed.

I wish OP would elaborate, not because I doubt them, but because the explanation is probably interesting.

I have a friend who occasionally works in a SCIF. My impression is that a radio receiver would probably be allowed, but an SD card would not. That’s what makes me suspect it has to do with sensitive equipment, though I’d be a little surprised any electronic equipment not explicitly vetted is allowed in that situation.