AnCaps are anarchists in the same sense that Stalin was a Marxist. They're merely capitalists who think they can rig the market more effectively without buying out whatever state happens to regulate it; they don't actually want anarchy, just a type of order which removes a chunk of the transitional layers between money and power. Note, in particular, that they don't reject the existence of organized militaries, police forces, courts, or even laws, just that they don't have sole control over them.
Well, either I'd either replace the first comparison with, oh, let's say mutualists (in the Proudhonian tradition) or the latter with Communists. AnCaps are anarchists and Stalin was a Communist, but anarcho-capitalism is its own distinct school from most other conventional schools of anarchism in the same sense that Stalinism can be distinguished from Marxism. And, in the same sense between the black or red schools of the left, you end up with "true believers" who immediately try to say "that's not *real* X" because it doesn't jibe with their own particular dialectical school of thought that, in its extremes, becomes almost Pythonesque (fitting, considering the infamous scene I refer to was in fact inspired by actual debates in the far left circles). Indeed, I think by your statements that they don't reject that list of things that you're confusing them, at least in part, with minarchy (basically paring down the government to the bare minimum); anarcho-capitalists consider the state in itself as a coercive monopoly. It's basically anarchy when you approach it from an extreme libertarian, rather than an extreme social (that is, in the sense of reciprocity and the exchange between equals) context.
Actually, apparently Proudhon was also a proponent of a limited state as well (to ensure worker's rights, rather than property rights), so minarchism does have a long history in the anarchist movement in general. I did not know that before compiling this post; learn something every day, I suppose. ^_^
EDIT:
Whoopsie, this is the Happy thread. Political debates are not happy. Political debates are the exact opposite of happy. I'll be going, now.