Here is a little extra detail. ABC, Fox, and ESPN are the broadcasters that selected 720p as their HDTV resolution. As far as I know, all the other broadcasters selected 1080i as their resolution. (Maybe there are a few exceptions that I don't know about. )
The cable box or the satellite box can be set to change those resolutions.Right now DirecTV is claiming that they are supplying 1080p, My guess is that they are using marketing speak and it's their box that's doing a conversion. At various times I've set my Comcast box to output everything in 720p, at other times I've had it output everything in 1080i. Right now I have it set to output the original native resolutions for each channel -- 720p, 1080i, and 480i. Our Kuro is doing all the conversion to 1080p for TV with this setup.
Direct TV boxes have the ability to set the output of video to native. Then you can go in & check all the resolutions that you monitor supports & it sends the signal to your tv & lets it handle processing/scaling.
As far as 1080p goes, it's limited to VOD only.
If they are providing 1080p via VOD, their sales reps, that hang out at BB, in our area are putting out false information. At least it's obscured information. They also claimed that Comcast was transmitting everything in 720p to their boxes. That's certainly not the case for Comcast in the San Francisco Bay Area. Is DirecTV's VOD a streaming service via the Internet?