This argument (that he tries to make several times in the article) does not hold.
Almost every time, the diagram is a _lower level_ representation of the program than the code is. And then he says "look! you can't figure this out from the code" (so therefore diagrams are better), but if the code was similarly represented in a lower level, you totally could.
And similarly, if the diagram happens to _not_ contain this extra lower level information, you can't figure it out from the diagram either.
I'm not saying diagrams aren't good, they can be great, it's just the reasons in this article aren't particularly compelling. But maybe I'm missing the point.