Fair enough, and I'll happily walk back that last statement until I read through that material. I have a fairly basic understanding of the commons, enough to get by, so I can always stand to learn more.
However, that does nothing to invalidate anything I said about private property. Exercising exclusive control over a resource, such as a parcel of land, your body, or virtually anything else, constitutes private ownership. This does not require nor presuppose a state existing in order to occur.