I see your point, but you're bringing your own assumptions about public and private here, and Twitter doesn't have to obey those assumptions (for clarity: I share your assumptions about public and private).
From another perspective, Twitter is an institution that makes rules to govern the conduct of its users. Those rules are made public, and users can construct their own order on top of those rules. This is pretty much the principle behind rule of law - we get to know what's allowed and what isn't, and we can then construct our own arrangements on top of this foundation. Some people came up with some creative ways of using Twitter's rules to control access to their tweets, which is exactly the kind of behaviour one should expect. Then Twitter changed the rules, invalidating the order that these users had constructed. They're upset, and that's not unreasonable.
Sure, there's a principled argument to say that "public stuff should always be public". Twitter's new policy makes tweets much more like blog posts - you can decide which blogs and comments you want to read, but you can't decide who reads your blog. I have no real problem with that as a policy. But it's still the case that Twitter, seemingly without warning, changed a policy in a way that broke social conventions that their existing userbase had developed. That's legitimately annoying for those people.
