Interestingly enough, there is enough radiation that you don't really need an actual connection. Someone put one of the endpoints in a field with a generator and got a connection to another endpoint. In a sense power line adapters are just using radio over the air.
Sending data over a power line, even at low bit rates is very difficult to do reliably. So all the radiation is in a sense a feature in that it improves connectivity. Not so much a feature to those who have an actual licence to use those frequencies...
Wouldn't ethernet cables have the same issues? Does the increased power flowing through power lines somehow amplify the signal? Is that pretty much the definition of what a power amplifier in a radio does, add juice to a signal on an antenna so it gets broadcast further?
Does the amount of wattage going through the line effect how "loud" the interference is?
In PLC (power-line communication), wiring is not meant to act as antenna. All transceivers are wired. It's an undesirable, unintentional side effect of limited (to the extent of complete lack of) cable shielding - because, well, power lines are usually meant for different application than data transfers.