Jeff:
Yes,checking the X10 protocol it seems that is a real case -- the schematic available seems to have a circuit with some capabilities to resonate and track the receiver circuit to the incoming 120 KHZ which may give some protection to the off frequency of the internal oscillator and this circuit may allow certain in frequency noise to resonate at the incoming noise .
Unhappily some inverters may be operating at a lower frequency with its harmonics falling within the 120 KHZ band causing HAVOC with the tracking receiver circuit , if the inverter output circuitry was not designed to clean all harmonics from the third up, the UPS and DC/AC inverter design that I have done, the output circuitry had the harmonics reduced to very low levels and for this 120 KHZ, the attenuation was better than 60 dbs, I do not remember right now those exact values, I had a lot of curves since the equipment was for the military.
In the past, we radio amateur operators played with some narrow spread communication and this seems that the designer(s) took some ideas to implement the X10 .
Nando