I'm afraid I don't know how the HMU's actually operate, but it wouldn't surprise me if they use mode S. When you look into all the other bits of rules you find that 99% of aircraft that are going to be RVSM approved are also required to have TCAS, and the TCAS equipment includes mode S transponders. Therefore there are very few aircraft needing a height accuracy check that don't have mode S. For those few there are alternative methods of accuracy checking using recording GPS units.
Hope this helps!