People most cite it as an argument for why you need hierarchies in your organization. However, I don't think the article gets to claim such thing. Instead, it claims that one should not let structure be implicit, because then it degenerates in tyranny.
People are too used to think that structure == hierarchy that we assume that the corollary is that hierarchy is needed to avoid tyranny. David Graeber in his "Utopia of Rules" [1] makes a good counterargument: if your goal is to avoid tyranny it's little difference to have it implicit or explicit. In the later case, you are just giving some moral justification for it -- you legitimize it, in the most literal sense of the word. What you need is, if you want to avoid tyranny, a resilient and explicit flat structure, with mechanisms in place to identify and reject emergent tyrannies.
I understand, though, why we are becoming disillusioned about the word "flat" in the business world. Most businesses that try to go "flat" still have a vertical ownership structure. What "flat" actually means in that context is: "you have to figure out how to make money for me, but I'm not going to tell you how!" This creates a lot of anxiety, because at the same time that workers are told to feel empowered and take responsibility, everybody spends so much energy in figuring out what are the invisible walls of the cell, and what their patrons actually want from them. I think it takes a lot of alienation to really thrive in such environment.
That does not mean that flat is impossible in the business world, in my view, you just need an explicit flat structure that begins with your ownership model. A company that I know of that has such structure is Igalia [2] (discl: I don't work with them but have acquaintances there)
[1] https://en.wikipedia.org/wiki/The_Utopia_of_Rules [2] http://igalia.com/