There are some rare cases where the fillings in peoples molars got radio reception. It's possible for any non-linear electrical circuit can demodulate AM radio signals. Slightly corroded metal fillings, or even an electrolytic connection could potentially do i. It's not that different from a crystal radio set. I repeat, it is possible for your tooth fillings function this way. It's just highly unlikely. If you were in close proximity to the transmitter and all the planets were aligned... There have been reports of this phenomenon since the early 20s. The names below have been changed because I keep bad notes...
John Smith of Evanston IL, lost a front tooth in 1961, he was fitted with a cap that was attached to the tooth stump with brass wire. Thereafter he began hearing music in his head, generally popular tunes of the day, usually while he was outdoors. He described the music as soft but distinct. He never heard an announcer's voice or commercials and was unable to identify what radio station, if any, he was hearing. After a year or two of this a new dentist put in a cap without a wire and the tunes stopped. BELIEVABILITY: 3 of 10
JANE SMITH also of Suburban Chicago, says in 1947, while she was riding a train from Cleveland to Rhode Island she heard radio in her head. The experience lasted maybe 10 minutes. She couldn't tell what station she was listening to but recalls hearing commercials and an announcer's voice. She had recent silver tooth fillings. BELIEVABILITY: 2 of 10
WFIU 103.7 Bloomington, IL
Due to the location of WFIU’s 100 foot transmission tower in the center of campus and its impressive 75,000 watt signal strength its RF "wake" became notorious. Students who lived in the surrounding dormitories reported they could pick up WFIU on their dental fillings, eyeglasses, electric shavers, etc. People claimed they could hear WFIU on their stereo speakers, even when their stereo was off. More here. BELIEVABILITY: 8 of 10
Today the toothradio actually exists. It was "invented" by a man named Andrija Puharich. He also was visited by space aliens and regularly ingested Psilocybin mushrooms and hung out with timothy Leary. He is not a complete loon, most of his other inventions relate to hearing aids.
The invention comprises an element applied to a viable tooth, for receiving RF signals and a transducer and a receiving element. It uses live nerve endings of the tooth for converting the electromagnetic signals to electric signals at audio frequency. It has US Patent 2995633. He made numerous improvements to the design until it was as popular among Russian spies as their trusty micro-dot camera.
In my world, things like these are called celibacy devices.