It is connected to cable, yes. It is grounded, and I've got a galvanic isolation piece on the antenna.
Pulling off the coax cable doesn't help anything at all with the buzzing, neither does disconnecting it from the receiver by unplugging the HDMI cable. Turning it off helps... On the 3808 this was not an issue at all, but here it is rather problematic. Tips appreciated - fortunately the cable company has a new model coming out later this summer, so I'm keeping the X4000, crossing my fingers and turning off the PVR a bit. Curses will occur when I forgot to turn it on afterwards.