Strange, never heard of this issue until this post. I got my xbox used as well, but it was one with the kinect. I have never really used or connected my kinect after my first day as I find it pointless and doesn't work well for me. I don't hear any coil whine. All I can hear is normal fan noise if I get really close to the console, not loud at all.
People are saying that an October software update should fix the issue. I hope they are right.