How it works: you can hear a high frequency wave if its modulated at audible frequency. If it's switched on and off at a relatively low frequency, you can sense the presence and absence of the high-frequency vibrations. Those waves are poorly absorbed from the air, but once they make it into the body they are transmitted much more easily by tissues besides bone. So your ears are not much better than the rest of your skin, which acts like a funnel for sound, diverting it to your cochlea.
I agree it might be unlikely that one signal might induce sound in a human that sounds like the sound a recorder might record - but I don't know. I just know that it's trivial for radiation to fool sound equipment (eg: cell phone signal too close to a speaker/mic/amplifier).
However, if this is a sophisticated weapon, there might be two signals: high power that target humans, lower power that target recording equipment?
There is also an easy way to test whether the sound is actual sound conducted in air or the effect of microwave exposure: ear plugs.