If anyone has ever seen a Smart Board, then you already know what I’m talking about. What it is is a board that hooks into a computer and a projection system and you can draw on it with special markers, manipulate objects on the screen like you would with a mouse, etc. Anyway, it’s a white board but there are real black pixels when needed and it definitely looks black, not washed out. How do they do this?
The same way they do black on a white movie theater screen: It’s not the absolute brightness of the given image portion, it’s the relative brightness of the portions surrounding it. The black parts only look black in relation to the image surrounding them.
You can likely see this provided you have access to said SmartBoard. Display a black image (or scribble black all over if that’s all you can do), and see what it looks like compared to outside the projector’s area.
Another analog: it’s similar to sunspots, which only appear black, until they are isolated. They only look black compared to the much brighter surrounding area.