All of the sudden we went from no rumors to a torrential flood of rumors regarding the next Nintendo console. Some of these rumors may have some validity, but because there's so many of them so quickly there's absolutely no chance that every one of them could all be true. You have to cut through the bullshit and try to guess which ones have some weight, and which ones are just hot air. Most of these rumors were likely just made up by people either due to wishful thinking, or as a hoax to fool people.
While its possible for there to be a controller with a screen, I can't buy that it would be an HD screen. Having a controller with a screen would be nice, because it would a convenient little HUD type thing which would be great especially in multiplayer games so you could see stuff that people sitting next to you wouldn't be able to see. But having that screen be HD would be overkill and would add more to the cost of the controller than it would be worth. Not even the 3DS (a $249.99 piece of hardware) has its display in HD, so its just not going to happen in a controller. I'm sure it would be superior to the black and white blocky VMU display thing the Dreamcast used, though. If anything, it might be based on the DS screen, because I'm sure Nintendo would have a bunch of these components available to use and the original DS screen would be more than sufficient for the task.