The signal transmitted via satellite by DirecTV and Dish Network is not the same signal transmitted over the air waves, which is what your TV is designed to receive. Each use their own compression technology to take the over the air signal and squeeze the signal to a smaller data stream. The HD signal you receive from a satellite system IS NOT the same quality you receive from an over the air broadcast.
Infact, the quality of ALL satellite TV signals is never as good as the original signal produced before the satellite companies retransmit the signal. They maintain a balance of channel capacity vs signal quality. The more channels added to a data stream, the lower the picture quality. Channel capacity increases subsribers, but signal quality suffers.
The real trade off is when you look at a SD channel on a HDTV. This is a HUGE problem for consumers. Some TV types work better at displaying SD satellite TV on a HDTV display technology than others. Plasma and LCD seem to offer less picture quality then DLP or LCD projection, when using a NON HD satellite receiver. If using an HD satellite receiver, you should always use the HDMI connection. It is the only way to carry a pure 100% signal from the receiver to the TV. This improves the picture quality of ALL channels, HD or SD.