There used to be stories, not entirely urban legend, of people who lived close to AM towers hearing the station in the wiring of their home, or in their dental appliances. Not impossible, considering that many AM stations broadcast with 50kW of power (like the one in this video) and can be received across a large swath of the country.
Reminds me of a Gilligan's Island episode, Hi Fi Gilligan: https://www.youtube.com/watch?v=3x1XHv0sxro
To give you an idea of how powerful that is, take a look at their coverage map: http://i.imgur.com/Aigz1Zh.jpg
The back story is kind of interesting. It was run by Powel Crosley - a sort of 1930's version of Elon Musk. Advertising revenues from the station were so successful he applied to increase the limit from 500kW to 750kW(!).
It's a big deal in the ham community, but I only learnt latter that while US stations were limited to 50kW - other parts of the world didn't have such restrictions. Parts of the Middle East have 2,000kW stations. [2]
You can get a full download on the Crosley WLW station in this video: https://www.youtube.com/watch?v=CbHjcwIoTiY
It's been dismantled, but I can imagine the number of ghost stories that it spawned. Just sitting in your house, and then you faintly hear a man speaking German...
I never heard the broadcasts through metal objects in the house either, but maybe they scaled back the power in the time I grew up there. Never heard any VoA broadcasts either.
It seemed that the signal path into the speakers was through the input wire (rather than, say, the power cable or the wires between the amplifier and the cone). From what I understand from my undergraduate analog signals course I'm suspicious of the signal actually coming from the transmission tower itself, unless the speakers had just the right configuration to act as a simple diode-rectifier envelope receiver (terminology likely to be incorrect), which I would think of as unlikely for an FM signal.
It may be that the signal came from some other path related to the relaying of the signal from the studio (~1 mi away) to the tower, but I don't know enough about the specifics of the radio station's configuration to say more.
I think I did eventually pin down which station they were picking up, but I've forgotten now. Interestingly, since I've moved to Switzerland, it's stopped. Maybe the signals don't get through Swiss customs.
That said, I didn't live 300m from 100kw...
(edit: I'm way wrong on the piano. arjie's correct about the backing track)