The ground loop is likely due to a difference in the ground plane between your system and the Directv system. Try attaching a wire from the chassis of the Directv receiver to your 975 chassis. The coax from your satellite dish should have a ground wire which is attached to the ground at some point. If this ground is not the same as the one for your house a small voltage can be set up which makes the hum.

I "turned it* waaay down" by doin' what the DTV install tech said not to:
routing the DTV through my APC H15.
* the noise

I also have a 975, and had a similar problem that was immensely frustrating. I tried a number of things, mostly focused on AC power and connections between the equipment. A ground loop isolator for the coax cable like the one above completely solved the problem - I highly recommend one, whether or not other solutions lessen the problem.

My apologies for de-railing this thread. Every coax isolation transformer I've seen advises against using w/sat TV. I plan to FIND the source of the problem - I know its in no way reflects on the 975 quality.

No worries. XenonMan is spot on; this is usually a difference in ground potential, and if you want to avoid an isolator, then you would want to:
If you have some thick speaker wire laying around, you can back off a chassis screw from each unit, wrap the speaker wire around it, and then tighten the chassis screws back down.

I have lived in several homes/townhomes where the ground difference was 6 mv or more and it is always the first thing I check. In my current house I had an issue and using a coax isolator did not solve the problem. I ended up using a 3 pin to 2 pin AC adapter on the AC for the TV. After unplugging and re-pluging each attached device, it was the Hitachi Plasma that made the difference. Since both cable and internet are coming on the same cable and I had a HTPC attached to the TV directly, I suspect I was getting a ground loop via the PC and its network attachment back through to the cable system.