It turns out this is NOT an isolated incident. I was reading about the Foxx tone Distortion pedal. A simple distortion pedal low on features but also low on price. It's a nice budget pedal with a good sound.
The story starts with this guy:
"I have a danelectro French Toast octave distortion pedal that recently has started picking up radio signals! I have substitued different guitars and cables and it appears when I turn the distortion up any degree it picks up radio. When I turn the volume control on my guitar to 0 it really kicks in. If I turn the distortion on the pedal to 0 the radio signal does not come in. I know its a crappy little plastic pedal that only costs 20 bucks but I would like to fix it until I afford a higher quality version of the Foxx tone machine. Any recommendations on how to repair or a new unit?"
What's happening is that the legnth of cord between the input and the guitar jack is behaving like a whip antenna. Depending on its legnth and the signal stregnth, you'll receive anything from shortwave to AM radio signals. Since the device is poorly sheilded and likely not well grounded even if it were, there is nothing to stop RF signals from entering the signal path. Before the guitar signal exits the pedal it's already intermodulated with the radio wave.
First of all this isnt' a problem at all limited to this make or model. In the studio it might be effective to plug into a strip with a broadband noise filter. You can also try shielding the plastic box with metal foil to block out the radio interference. You can use aluminum tape inside the chassis to keep the mod invisible (dont forget to ground) and not marr the nice design. You can also try wrapping the cables through toroids, that'll cut the noise from the ungrounded circuit and clear that radio reception right up.