I have an "HD compatible" TV. I understand that to mean it doesn't have a built-in HD tuner.

Do the DVR from these companies have built-in tuners, or would I need some kind of dedicated tuner to get HD broadcasts?

Do the DVR from these companies have built-in tuners?Yes. They all have tuners which will receive their own HD programming. But only the satellite companies' tuners include an over-the-air tuner (in case you also want to use it to get your local OTA's with an antenna).

You can also purchase standalone tuners which can receive the local HD/SD digitals through cable (QAM tuner) or OTA (ATSC tuner).

That's what I was after. Thanks for the info.