USB is not immune because it uses differential signalling.
The benefit of using differential signalling is that higher data rates can be achieves because noise is reduced by utilising the high common mode rejection ratio of a differential input amplifier on the receiver end of the cable, any radiated noise received in the cable is common to both positive and negative signal lines because of their close proximity and twisting.
That is, the differental signalling concept is used to increase the speed of transmission.
You're still going to get radiated emissions from the cable.
The detection techniques rely on two principles:
radiated noise in the form of RF
conducted noise back up the power cable.
I think you'll find you will still get high frequency noise superimposed on the power line, albeit very small in amplitude. Sure, the power supply contains inductors, and if in series with the power line will provide a high impedance path to high frequency signals, but it's a high impedance which results in attenuation, it's not infinite attenuation.
You'd need to start adding appropriately designed filters on the power lines to suppress the conducted emissions.
If you really want to prevent people spying on you using the techniques then you need to start adopting TEMPEST principles and taking to the extreme, everything would be house in a Faraday cage, a big metal box, ie..a room with no windows, metal doors with berillium copper finger strips space close together down the edges of the doors to provde 100% continuity of screening.