Hear me out, before HDTV and similar HD theatres, digital quality was perfect. It was something you can playback on both your home entertainment and computers. Whenever I watch something HD on computer it looks all blurred.
Now digital photography and digital camcorder videos on Youtube are actually of better quality than some of these TV shows and movies.
The main factor in HD quality is the number of bits alloted to a channel. If you compress it to lower bitrates you get lower quality. So, sure, various providers may squeeze feeds to get more on their satellite or cable or other medium. So it depends on the carrier - you have to figure out who to complain to on this one.
I have heard a ton of people say this, and then it turns out they just didn't get an HDMI cable.
You NEED the cable to actually watch things in HD. In addition, the source material must also be in HD.
Just like a color TV won't turn black and white film into color, an HD TV won't turn standard definition video into HD.