FM broadcast is propagated over the UHF range, so your guitar is able to pick somewhere in between 300 MHz and 3 GHz
To pick up some sort of radio signal, you'd need a length of metal connected to an inductor and a capacitor to fine tune it. Of course, it takes additional components to reduce the noise

I think your guitar has a a circuit that contains those components!
You can create a simple transmitter and receiver circuit out of 5-6 components (good for peer to peer communications or clandestine bugs). In fact, you can also create a battery-less FM radio receiver circuit that is used with a headphone!