I think that the basic element of the quote is that the notion of justice has to be experienced and asserted from the most individual point of view. Society cannot look to institutional leadership to fully define what justice is. In the event that individuals occupy power whose ends are not just, the definition of the concept becomes perverted and twisted. It is for this reason that individual moral and ethical conscience becomes the fundamental chamber from which justice operates.
Miller certainly would support this with characters like Proctor and Corey. Giles Corey recognizes that the established political order of Salem in the form of Danforth and Hathorne wants him to "name names." Yet, he understands that the implications of such an action is to not further but rather deter the ends of justice. It is for this reason that his conscience becomes the basic chamber of justice in that he represents how justice becomes rooted in the individual, perhaps even before it is rooted in social or political orders. Proctor is much the same way. In his closing speech, he acts to save his name, something that becomes associated with "justice" and the idea of serving the ends of fairness. In refusing to give lies and "subscribe" to them, his conscience is the realm in which justice becomes the foundational chamber for all advancement. It is here where I think that the quote becomes very meaningful and relevant in that individual action is the domain and the citadel where justice arises.