How can power line devices be affected by a power supply?
Power line communications have an uphill struggle. Firstly they have to "fight" against the massively bigger voltage of the AC supply. It may be 110VAC or 230VAC normally and the AC is going to be between 10 times and a hundred times bigger than the signals used for communicating data. This is mitigated by the data comms being modulated onto a carrier frequency that is much higher than AC power however, fairly complex filtering is still needed to seperate the data from the AC in the receiver.

Add to this is the noise taken by loads such as TVs, washing machines, computers etc. and reliable data comms is made even more difficult. Result is that data rates reduce because of the need to retransmit packets of data that become corrupted.

Modern power supplies nearly all use switching regulators and these can generate a whole bunch of interfering signals across the spectrum. There are regulations governing how much noise switching power supplies allow back onto the AC power lines but I guess cheaper ones will not be as good and therefore cause more data corruptions which leads to more data packets being retransmitted which leads to lower payload data rates.