The sound may be caused by an earth loop. This is similar to feedback when a mic is placed near a speaker, in this case the loop is through the mains connection to the camera and the mixer board. It is not uncommon and can be difficult to remove. Suggest you run on battery while recording.
I was recording a high school theater performance the other night. I had the sound coming out of a SUB out on the mixer board, and that feeding into the mic input on the camera. I notice that when the camera was running off the battery, the audio sounded just fine. However, when I plugged in the power adapter, there was a lot of noise in the audio. Why is this?