You shouldn't be surprised given the challenge restrictions. You have pure white and pure black, so the most logical choice is something right in the middle to equally benefit both colours.  If you choose a lighter tone, the black seems too dark, and if you choose a very dark tone, the white is left useless. As for saturation, an oversaturated colour would not fit the other two, since they create a grayish image. 
Gosh, I talk too much about silly things. Thanks for the comments, guys. And sorry if my dithering is a little sloppy, it's just not my thing.