In that case, I would frame it like this: Authority does not create, nor does it dictate justice.
Justice exists regardless of authority. Or, rather, it is a matter of morality, not whether or not someone in power dictates their will to you.
Authority is a tool, if you will. A spoon does not come from the carving knife, but that carving knife can be used to make a spoon.
Justice does not come from authority, but it can be used to achieve justice.
A carving knife is not guaranteed to create a spoon.
Authority is not guaranteed to create justice.