The 12V outlet on the dash is probably not clean power, but there could be other sources of interference, considering all of the other electronic equipment in the chassis.
Does the frequency of the hum change with engine RPM? That signal could be coming from the ignition system or the alternator. There are installation methods to filter this particular interference to ground,or to block both signal sources, usually applied to the wiring for the OEM radio.
It is also possible that something in a nearby part of the spectrum, or a harmonic thereof, is getting into the satellite signal, but that should interfere with reception more than it injects noise. That's way out of my experience, I was working on what were the problems 50 years ago, we weren't trying to pick up signals from satellites.
The problem can be also be in the speakers, if it hums and buzzes regardless of signal source, and that can be as simple as mechanical connection problems.