You have to use DirecTVs receivers to get their service. Specifically, in order to get HD service you have to use their HR2x models (HR20, HR21, HR22, HR23, HR24) for HD-DVRs and H2x models (H20, H21, H23, H24) for HD receivers.
There supposedly is going to be a new Tivo unit released that will work with DirecTVs service, but I wouldn't count on it until it actually shows up. They have been talking about it for about 3 years now, and keep pushing back the supposed release date. There still hasn't even been a working unit (or even a mock-up) shown to the public yet.