I have in wall and ceiling klipsch speakers. I get a clicking noise when watching my dvr, usually network tv. I haven't really noticed this live or in any other format. It's also usually the ceiling speakers. I have moved the surround to just the front and it still ticked, but only on recorded tv.
I haven't experienced anything like this but please provide more detail such as dvr mfg/model, source of network signal, receiver/amp, etc. If I understand you correctly, you've swapped speaker outputs at your amp and get the clicking sound specifically through your remote speakers, not from your amp? It sounds like an electrical interference - are your components plugged into a filtering device or just plugged into your wall outlets?