Definition of Anarchy
Any society in which everyone is expected to follow the NAP, or be subject to the usual social disapproval, is an anarchy.
Proof
State actors must violate the NAP in the course of their duties, as otherwise they would be unable to force compliance.
The reason that it is possible to find people to do this is that the vast majority of people believe that it is right or at least acceptable to violate the NAP if one is acting in the name of a State.
This is necessarily true because the only difference between the behavior of a criminal and that of a State actor is this different expectation on the part of the general public: that while it is not acceptable for a criminal to violate the NAP, it is acceptable for a State actor to do so.
So if there were no exception to the rule of following the NAP made for State actors, there would be no State.
Q. E. D.
Note regarding NAP violations
Note that of course this does not mean that there would be no NAP violations in anarchy; of course it is likely that there would be, because some people are criminals. The sole (but immensely important) difference is that no sanction would be given to these violations, so they would be far more expensive to those committing them.