I don’t know who’s interpretation of Anarcho-Capitalism you are following, but since ther has never been an Anarcho Capilist government in the world (which sounds ironical) it’s all just ideas and interpretations, of which seem you are grabbing the worst of the pile.
Rothbard’s definition includes in the fundamentals of the Contractual Society being voluntarily approached and free of violence or harm, which is to say that if you do not respect the inalienable rights of the others, you are violating the Contract for being in that society, and you are rightfully gonna be aprehended. There is no contradiction
Also, to what you said about “demonstrated” something, mind linking to what you have? There’s nothing around here like that