If you think about it, any antenna picks up virtually anything from a few kHz to over a GHz - all these competing signals arrive on the input stages of a receiver but the receiver does what it does best - it focusses on the frequency band it is interested in and largely rejects everything else.
Clearly a big signal just outside what it focusses on can have an effect and these are known phenomena to radio guys.
Using a headphone audio wire is no different - the audio is never really anything like close to the frequency band of interest for the radio so it barely breaks a sweat rejecting it even though it might be a few volts peak-to-peak whilst the real signal received might be a few micro volts.
A single-order 1 MHz high pass filter will provide 120 dB rejection to a 1Hz signal. A 2nd order 1 MHz high pass filter will provide 120 dB of rejection to a 1000 Hz signal. A third order will reject 10 KHz at 120 dB and so on and so on. The filter in a radio is probably equivalent to a 6th order at least.