You say the noise is there when you're receiving a transmission and actually reduces the signal strength - I'm assuming you do mean signal strength, and not just readability, and that the noise isn't there when there's no transmission.
This sounds like modulation noise. That happens when the radio signal is getting into some part of the electronics and being modified before getting into the radio's signal processing chain. In domestic receivers, it can sound like a loud hum that only appears when a station's tuned in -- in such cases, the mains rectifiers are getting the signal from the mains lead, modulating it with the mains frequency, and then propagating the resultant mess back into the radio. You can also get similar effects when a completely independent circuit has a fault that makes it marginally unstable, and the radio signal either tips it over into instability or combines with an oscillation or noise source.
Diagnostic characteristics include the problem getting worse (or only appearing) at strong signal strengths and often going away completely for no apparent reason. It needs quite an obscure set of circumstances to kick off.
I think the chances of it being connected with power regulation are high, as such circuits do have a good ability to become wideband, powerful noise sources combined with lots of non-linear junctions that make good modulators and plenty of long wiring runs that act as antennas. Plus, although it's a rare beast, you do seem to have eliminated everything else!