The hangup here seems to be the definition of "program". I'm using it to mean something roughly like "executable", which I think is fairly close to what the original article meant it to mean. You seem to be using some concept of "program" that makes each of busybox's functions a separate program. As far as I'm concerned, on the other hand, busybox is one big program that does a lot of largely unrelated things, choosing which of them to do based on how it's invoked. There's no right answer. You could say that all of the software running on a whole computer is one giant program, and in fact sometimes I do find it convenient to think of it that way.

I don't know that your definition of "program" is wrong, but I do think it's alien to this context.