Earlier quoted context omitted.
I am in no way confused. The three color components of an LCD pixel are not in the same spatial location. Look closely and you will find three rectangular areas, one for each color. The only colors you can make without combining elements are at the 2^6 or 2^8 variants of red, green, and blue. I subtract two because (ok, I am confused, I only subtracted one before) because the blacks are all the same.
1. If you're seeing the RGB elements separately, you need to sit a little farther back from the screen. :) I can't pick them out individually at all (I can just barely see the pixel grid with the screen an inch from my face), so it's not particularly useful to think of color this way - because nobody sees it like that. 2. Even ignoring this, your numbers are still wrong. 2^6 = 64, and 2^8 = 256.
2^6 = 64, but I have red, green, and blue pixels, so times three, but subtract two because all the blacks are the same.
I suppose I'll need to write a small article on this with some pictures. In the process of researching this I was impressed with how useless macrophotography of a screen was. Small changes that are obvious to the human at a distance are invisible when looking at the individual r,g,b elements up close.
I'm away from my camera that can output RAW data, maybe with it and some numerical image analysis I can tell if there is multipixel dithering going on, but my human eye isn't going to tell, even from magnified pictures.