It's still speculated... see:
I don't have any idea how it'd work, much less how the signal would be demodulated... However, I'd like to play devil's advocate and point out a few things... first is that tissue does not make a good faraday cage. You are a better conductor than rubber, but MUCH worse than copper. UHF and VHF passes through you relatively easily.
Secondly, do you want to assume that, if this legend is true, the filling induces sound in the mouth? Electrical impulses transmitted around your auditory nerve definately seem like sound to the beholder. Maybe that's the mechanism...?
Lastly, who's to say the filling acts as an antenna, a diode, or a battery? A filling in a saline solution, surrounded by nerves, bone, and other tissue might act completely differently than it would stand-alone.
I dunno if it's true or not... it'd be interesting to get concrete proof.
Dave