Another crack at an explanation:

The goal of the Zone System is to capture as much of the scene as possible onto the film, so that it holds detail in both the shadows and highlights. In effect, you're making a "master copy" of the scene. These zones are 1 stop apart.

However, paper has a narrower range of reproduction. Think about trying to interpret a Rembrandt with Crayola crayons: it just isn't going to fit, visually, since you can't reproduce all the range of colors. Paper is similar: it won't reproduce the entire range of textures you have on the film, so compromises have to be made somewhere. So, a one-stop difference on the film "master" may be more narrow on paper. So of course if you then scan those tones on the paper, they wouldn't translate back to one stop between themselves.