I just received my second 8x because the first had this problem.
First: if you don't own and HTC 8X, it's hard to understand the real issue, and even harder to understand the actual discolouration. In fact, I can't understand the discolouration myself. All I know is; I love the 8X and I was obsessively careful with it (I always am with new tech). The colour issue seemed to pop up out of nowhere, while the rest of the phone was immaculate. It was clear that it was some kind of fluke, or design flaw.
Second: I have tried a couple cases with the phone, and am even currently looking for more, but the reason I bought this phone over the Nokia 920, was because the the design. I wouldn't have considered buying it if the hardware and performance weren't great, but it was the colour, and design of physical properties that initially drew me to it, and ended up sealing the deal. Not only is it great to use, but it's great to hold (Just like the HTC and Windows Ads say.) I knew I would have to handle it carefully, and I did because I absolutely love the design. A design I don't want to change with a case. Some of the 920's features are better, and I probably would have gone with Nokia if they'd advertised the 8x in a Case!
Third: Beyond everything else, I want to understand the specific cause of this, so I can prevent it. I think the most plausible answer has to do with the soft touch sucking up dye. I do have one Question. How many of you have applied a screen protector that came with fluid: Armorshield, Zagg, Skinomi, etc... I only ask because I don't know what the fluid is, and I noticed the discolouration after I applied my second screen protector. The edged and the corners are where I wipe the excess solution from and the cloth that comes with the Armorsuit is black. Could this be a cause? I only ask because I am thinking about getting another clear armorshield to apply to the entire device, which would effectively protect it without altering it too much.