It makes sense, the DAC is in the monitor, but the monitor is an electrically noisy place, so the IC that's responsible for the DAC/AMP is picking up noise from the power circuitry in the monitor. It's common with cheap DAC/AMP chips, like what they use in low end motherboards and monitors.
Basically as power usage is increased the noise should be greater. Unfortunately it's a design flaw, so your only real option is to replace it to resolve the problem. You may see improvement with a ferrule, or you could try doing some hardware hacking and adding shielding around the audio circuitry.
The ferrule is the easiest and cheapest, but it may not fully resolve the issue.