I believe you would have to use a DISH Network tuner box with an analog video capture board. As long as the tuner box accepts commands over a serial link, you should be able to have MythTV change the channels.
I don't know of any boards that work with MythTV that support satellite or digital cable. Only broadcast tv, analog cable or over the air HDTV. In order to get satellite or digital cable, you need a tuner box for the system.
Dave
Dave,
I found this How to, that supports what you said and provides a way for Dish Network subscribers to make and use their own MythTV system:
http://losdos.dyndns.org:8080/public/mythtv-info/MythTV_DISH_IR_LED_TX_via_M...
Ed