To be clear: My point isn't that there's breaching between the two categories. Obviously, no category we use outside of the most basic are going to be ironclad. My argument is that this idea assumes that the polity is the only source of institutional power in society, or to be even more acute, solid institutional power. But virtually no one assumes this as a matter of course.
Why do we assume the political institutions of society are the only "public" forum? Yes, they're the only "public" forum that constitutes everyone inside the borders of the nation, but those borders are totally arbitrary. If I work in a corporation that I "choose" to be in (but I also "choose" to continue living in a country), that is a forum that I do things in, help make decisions in (even if those decisions are simply in what direction I move my mop brush), etc.
The reason this dichotomy is made so stringently by Friedman-esque advocates is because it lets them focus inerrantly on state oppression. Again, to be clear: My argument is not that state oppression is not serious. Indeed, as an anarchist, I advocate the replacing of the nation-state with a radically libertarian polity. But I also believe power can incarnate in a variety of drastically different, indeed qualitatively different, forms. If the dichotomy is constructed, capitalist advocates can concede that a lot of things may or may not be bad (i.e. "Yes, people suffering does suck, and maybe we should give them money or have charity"), but no governmental intervention is needed or justified. After all, private actors get leeway public actors don't. QED. (And, by the way, I am somewhat receptive to this stance). What are the responses?
1) Even if this is the case, it's a massive irrelevancy. If I can prove that the internal structure of, say, a corporation is illegitimate, then it is the ethical responsibility of the people inside it (particularly the people with control over policy) to alter their decision making process. Every reasonable rights advocate recognizes that rights are separate from ethics and that someone can have the right to do some unethical things (say, advocate unethical principles or insult people).
2) If institutions perpetuated by society are unjust, those institutions are public tyranny irrespective of whether they occur in the economy, polity, etc. Yes, one can imagine rogue institutions that are illegitimate yet are private actors (and the upshot of this is that there's not a whole lot the polity can do about it), but one can also imagine institutions encouraged by the other primary institutions of society. Corporations and markets are given legal status and other institutions denied. Increasingly, as a practical matter, economic and political institutions are becoming intertwined (i.e. revolving doors, corporate control, etc.) and homogenuous (i.e. the restrictions put onto states by organizations like the IMF and treaties like NAFTA).