For example, if a bright red object and a bright blue object use the same tile, the tile can use bright red for all pixels that only the red object uses, bright blue for all pixels only the blue object uses, and bright magenta [....] for all pixels both objects use. In this fashion the two objects that share a tile would look completely different. In practice however, this is probably impossible because so many objects share the same tile, the chances of the potential foreground colors sharing a red, green, or blue color component are too great.
So it's impossible to work with combined colours because so many objects share a tile, but you can work with combined colours when two objects share a tile. Does that mean it's not tile-sharing per se that's the problem, but the sheer number of individual objects that can be attached to a tile?
Is there an example that neatly illustrates the use of colours that aren't magenta or shades of grey? From that article, I don't understand the point of using other colours at all.
The connecting + tile is used for doors, designating engravings, and stationing squads. Doors have white foreground and various backgrounds, but the others are always cyan on black. Cyan × Red is black, so any red pixels in the tile will show as black in the cyan object.
You could use this to make a red door around a white +, so designations wouldn't look funny, but then all the details on your doors would have to be shades of pure red.