You can't use a color picker see color fringing due to subpixel rendering. (There's tons of info about this for font rendering). Your display doesn't map pixels 1-to-1 in most cases. But like I said in my edit, I'm fairly sure that part is irrelevant here.

The blue/gold dress was not related to screenshotting and compression. People were arguing about the color even when looking at the exact same image. It all depends on which color temperature the dress was lit with. Noone can know for sure, and your brain just picks one (maybe depending on the room you're in).

It's the same sort of deal as those rotating optical illusions. It's possible to see it both ways, but your brain usually picks one and it's hard to switch.