That's just semantics, for all intents and purposes the monopoly on violence is exactly that: the monopoly on the legitimisation of violence, only the state allows violence, you can only perform a violent act under the provisions the state allows, hence it's de facto and de jure holding the monopoly on violence.

Stating this because I'm not sure what differentiation you are trying to achieve with the semantics game, the meaning is the same for any interpretation.