Almarg, is it possible that a power cord can act like an antenna? Remember that we used to use wire inside a plastic covering to pick up radio signals for our tuner.
People do sometimes have problems with phono inputs picking up radio signals, due to the very high amplification that follows, the highish impedance levels, and the fact that those lines are directly in the signal path. In fact there are two threads presently ongoing here involving that kind of problem.
But it seems extremely unlikely that a similar situation would arise with a power cord. First, impedance to ground is low, which would tend to "short out" any rf that was being picked up. Second, there is no subsequent amplification. Third, there is no direct path between the ac input to a component and the signal path. Assuming the design is well done, the power supply section would include filter capacitors that have good performance at high frequencies (in addition to the large electrolytic "cans" that provide energy storage and ripple filtering but don't do much at high frequencies). And the amplifier stages themselves presumably all have "decoupling" capacitors that filter out high frequency garbage from the power going to those stages, right at the point of use.
Regards,
-- Al