It is most likely the processor in the receiver. The remote controls are an unlikely source when not in use. These new boxes have more in common with computers than anything else now, so the steps to reduce interference will be similar to what you would do for a desktop PC.
To isolate the problem, turn on the DirecTV rcvr. and an AM radio. Then start disconnecting one thing at a time (phone line, connection to TV, connection to dish, etc.) to see which cord is throwing the noise. If it's none of the above, then the interference is being sent thru the AC wiring (especially if the unit does this when it is turned 'off'). Also make sure all coax connections to the dish are tight, and that the dish is properly grounded. DirecTV boxes tend to be fairly well shielded, so I'd look at the phone line first, then the AC cord. This may not eliminate the noise 100%, but will cut it down. RatShack has snap-on RF chokes. Follow instructions for proper installation & number of windings.
Also, some surge protector plug-strips have RF filters built in. Look for one and use that too. Every little thing helps. (Surge protection is always a good idea for DBS boxes)