We could discuss it further I suppose, but it's somewhat dull well-treaded material IMO. Anything about the definition of anarchism is up for debate of course, but completely un-checked capitalism certainly does not inherently result in a society that fits the criteria. What could possibly be anarchistic about a society full of wage slaves? That's certainly one likely outcome of such a society (note I'm not saying it /would be/ the outcome). Corporations can - and do - coerce every bit as much as the state does, if not more.
If you're an anarchist and not a socialist, fine. The term "individualist" works well. It's not the ideas of free markets and commerce, it's the /term/ capitalist. The word itself is pejorative. Anarchism is traditionally a leftist movement that came from the same kind of time and place as communism - "capitalists", the class, are the enemy, and exploit by definition. In the world of political discourse in which anarchism lives, If you call yourself a capitalist, you are essentially saying "I exploit others who actually do work as my source of income". You are NOT saying "I think free economic exchange is a good idea", which is probably what you actually mean to say. If you want to have serious discussion with anarchists, you can't call yourself a capitalist. All you will get is endless tirades about why you are not an anarchist, like this one. You might as well show up at a hard right think tank and call yourself a libertarian-stalinist.
You also hinted at the acceptance of individualist anarchists. Correct me if I'm wrong, but anarchists have no problem with the coexistence of different communities, each with their own flavor of anarchism. The difference between anarcho-"capitalists" and other individualist anarchists is not very large, and is one of degree. Once individualist anarchists are accepted, only semantic issues prevent the acknowledgment of these other anarchists.
But I agree with you that it's a big source of confusion for them to call themselves capitalists. It also doesn't help that some of them describe themselves as being right-wingers.