You're probably going to have to read off the faceplate of that "splitter" that's in your "cable box" and tell us what it says. The fact you have just one line coming from the dish suggests what's known as a Single Wire Multiswitch installation. You still can't use regular cable splitters with that, but IIRC it can be configured to work with multiple receivers in the same room being fed off of the one line, assuming THAT line isn't split upstream. Note: I don't have an SWM installation, so I don't have hands-on experience. I'll fix the title and maybe drag some SWM experts in here.
I, too, have 4 - 5 sets on one wall of my basement for weekend sports. I have one cable box, three D* receivers and one HTPC. Every set on the wall can display DirecTV, cable or over-the-air. Even internet streaming via the HTPC. It's a nice setup, but required fishing a lot of cable, since each D* receiver has to have its own cable back to the multiswitch (in my case, a Zinwell 4 X 8) but the end result is nice. The 55-inch set displays whatever game we're paying rapt attention to. The other 3 - 4 sets will have other games, RedZone, NASCAR or what have you.
And, yes, D* receivers can be configured to work with different IR codes so they don't conflict. In my arrangement, I have one receiver using IR, one using RF and one that's a different brand altogether.
Grab a picture of your dish and of the box its line runs to.
Oh, and by the way DTV = over-the-air digital television. D* = DirecTV. Just some conventions we use here on AVS. No biggie.
Walking the fine line between jaw-dropping and a plain ol' yawn.