Dual Tuner question

I have an HD DVR dual tuner. HD shows in the den, the TV in my bedroom is TV 2 on that receiver. It is hooked up via a coax. The HD menu shows up on TV2 though. If I purchase an HD TV and run a long enough component cable or HDMI cable (prob have to be 30 feet or so) from the receiver, would HD show on TV 2? Customer service live chat said no, but I am not so sure. I can see the HD channels on the SD tv, but the sides are cut off bc the screen is not big enough.

Any thoughts?

If you ran the cables from the receiver, yes they would show HD but only tv1 outputs HD which means both HD tv's would be showing the same program. Tv2 outputs do not include HD, you can view HD programing but not in HD.