Insane that there are people denying that this happened. I wasn't born during this period, but being able to download stuff off of terrestrial radio is completely believable. What do people think Wi-Fi or cellular networks are???
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It's not obvious that the frequency range used by computers recording on audiocassette would fit into that used by AM or FM radio transmission and reception equipment.
In other words, it's obvious that it would be possible on equipment specifically designed for it.
But I'm quite surprised that it worked without it (presumably) having been designed for. Or maybe they did pick a frequency ceiling compatible with commercial radio intentionally?