I just picked up the HDHomeRun Dual and as I understand it, you must have at least 1 PC running MCE in order for the HDHomRun to work. I'll try to explain:
Content (either OTA or via Cable) > HDHomeRun via RG6 cable
Network cable (Cat5e or greater) from Router/Switch > HDHomeRun
PC w/ MCE > same router/switch (hardwired is preferred, but wifi is OK)
Xbox360 > Same router/switch.
The way the software works is that your xbox is controlling the tuner via your PC. so the "signal" to change the channel from your xbox goes over your network to your PC, then from your PC, it sends a signal via the included HDHomeRun software over the network again to the tuner inside the device. Voila, you now see a new picture on your screen. The above is how I have my system set up and working. Everything is hardwired as well.
Obviously this is a gross over-simplification, but I hope it helps.