Update:
I tested my 721 at another person's house, and it didn't have any problems with incoming calls. I just took it over there, plugged in the AC, waited a few minutes, plugged in the phone line, and called - the phone rang perfectly.
I tried the same procedure at my house, but with the phone line hooked DIRECTLY to the jack in the DMARC outside my house (so there were no other devices connected, just the 721) and it still did it.
According to the people I talked with in ATR, the fact that it happens even with no sat cables hooked up eliminates grounding as an issue, and the fact that I hooked it up to the DMARC eliminates additional equipment-caused problems. I tried it with and without DSL filters, so that's not the problem, and I tried reversing the phone wires (polarity) and that didn't help either. Plus the offsite test working eliminated the receiver as a problem.
They tend to want to blame to phone company, and I want to blame DISH. Sure, there must be some slight variance in my phone line, but if all my other phones and modems in the house and computers work, the issue is that their components or the drivers/software is poorly implemented!
So... any ideas?