I think that a long time ago, both DirecTV and Dish Network used the same technology to receive their satellite signals. At that time, their dish's where interchangeable. But over the years, Dish has advanced their tech to include Dish Pro and Dish Pro Plus which supports longer Distances, better switches, and even dual tuners over a single coax feed.
So Dish can still fall back to the older tech, but the DirectTV receivers would not know how to handle the newer Dish tech.