I'm talking about how it looks if the box partially covers other content.

A 1-dimensional, 1-sided horizontal example would be if you have abcdef in the background partially covered by ABCDEF in the foreground. With a vertical bar in the middle, it looks like

    abc|ABCDEF

However, with this new technique it looks more like:

    abc |ABCDEF

(approximation, notice the space; also this example assumes a different stacking as used in the article, which brings the problem in the x-direction which is convenient in this example)