I always hear this in discussions about number stations, but I don't think this is true in the US. In fact, I don't think I've ever seen a general consumer "shortwave radio". Unless the regular AM band counts, which seems to be medium wave.
The younger people I know tend to own such a radio in the form of the Baofeng UV-5R or the like.
However, carrying one of these is probably highly suspicious compared to a world band radio receiver.
I don't buy it.
Satellite downlinks are broadcast to everyone under a potentially massive footprint. Take a look at the footprint for QO-100 which you could use with very inexpensive equipment that looks pretty much like a normal satellite TV dish.
https://jeremyclark.ca/wp/telecom/sdr-for-qo-100-satellite-r...