Firstly, I don't think any capitalist society exists and I don't think that should be very controversial if we're taking the meaning of terms seriously.
Secondly, you're right about there being different views of ownership and I would consider a society to be capitalist if the only government actions were either voluntary or seeking to resolve property claims between private citizens.
Thirdly, an entity that settles ownership claims would have to get its resources from consenting people in a capitalist society (or produce them from natural resources).
Again, I'm talking about the meaning of terms. Viability of systems is a different subject. If you want a long ass reading list for how a capitalist society could work, I can provide that.