I agree it is very unlikely. And I don't think you are proposing this is the case, but for the sake of argument. However, wouldn't it still be rather easy to verify? Faraday cage just helps with isolation and filters out the noise, so you can analyze a smaller set of data, in this case meaning you have to parse through less signals/data. But you would still be able to pinpoint this. If you can just monitor ultrasound, filter out what isn't easily explained/common (like background background radiation is to the universe).

To verify the original claim that it could happen over BLE, you don't need a faraday case to verify or prove this. The faraday cage just allows you to cut down on the data/signals to analyze.