DirecTV offers HD feeds for almost all of its channels, so you should not have the problem to start with. However, much of the problem you noted with stretched images that "look like 400 pound NFL linemen" is the setting on the television as opposed to the service provider. You can set the TV to fill the image area with the picture, which will stretch an SD 4:3 aspect ratio image producing the image you refer to. Or you can set your TV to not stretch it, and you end up with a smaller, roughly square image in the middle of your nice wide screen TV which is not distorted. It's just not filling the screen.
So, showing any proper HD feed, you should get full screen, non-distorted, images. Showing any non-HD 4:3 aspect ratio feed (SD channels), you have a choice. Full screen stretched, or less than full screen proportional.