"Yes and when I hit my radio with a rock it might stop working, change the station, if I rip out transistors it might make the sound distorted, etc. That really doesn't prove that the song is stored inside the radio, does it?"
Pace Dan, above, it would not be "parsimonious" to assume the song is "stored in the radio." Even assuming complete naivete about how radios work, it would be relatively easy to show that the songs are (in some mysterious way) coming from some outside source. (For example, you could compare the performance of two identical radios as one is systematically banged up -- although just the fact that two identical radios set next to one another play the same content in perfect simultaneity in itself would be suggestive.)
What's fatal to the analogy, then, is that while physical abuse to your radio doesn't qualitatively affect the radio transmissions, physical abuse to your head does qualitatively affect your mind.