No, the DirecTV Phase Three Dish's are NOT compatible with Dish Network.
First the DirecTV switches are NOT compatible. Second the 110 LNBF on the DirecTV phase Three Dish is a NON standard DBS LNBF that can only receive three transponders 28, 30 and 32 (those three transponders have to be remapped so DirecTV receivers, can see the 110 transponders, which are not capable of receiving Three Orbital slots). 110 LNBF on the Phase three dish remaps those transponders so DirecTV's receivers are fooled into thinking those 110 transponders are really coming from 119 on different transponder frequencies.
Has anyone done a side by side comparo with the D1000 and Phase III? Its been a little while since I installed a phase III, but the D1000 sure seemed.....familiar.