This problem is very common, and does not reflect on the design of the speakers. The audio/video industry has been plagued with complaints of this nature for years. The problem is the speaker wires act as an AM antenna. The AM signal is picked up by the wires, and sent to the amplifier to be amplified along with the intended signal. If the pre-amp stage has a noise gate, like the inputs on the Apple Powered Speakers, the amplitude of the AM signal is usually not high enough to pass the gate, and it is not amplified.
The only thing that can be done to alleviate this problem is to purchase some higher quality shielded cables. Two possible sources are TASCAM and Monster Cable.
Again, this is not a design flaw in the speakers. Apple is responsible for designing equipment that adheres to Federal Communications Commission (FCC) regulations, and have done so with the AppleDesign Powered Speakers.
Another option is to log the interference complaint with the FCC. The FCC is the governing body for Radio Frequency (RF) emissions in the United States.