In anarchist literature, statism generally means the ability to confer and legitimate violence. Now, generally speaking, they were talking about physical violence, in particular the killing of peasants revolts (one of the things that they criticized the Soviets, correctly, for doing, even though I don't know if an anarchic state of affairs would have been able to withstand the challenges of white army invasion, neither here nor there). However, the idea that a private land owner (a contradiction already within an anarchist society, but we'll continue for the sake of argument) has the right to exercise full control of their land without the consent (or even in defiance of) the general community, is not anarchist praxis.

Basically, you can throw all the trash you want, but you cannot tell people they can't come and pick it up.