Excellent point.
The problem in English is that we use the noun "justice" to both describe functions and departments of the legal system but also as a synonym for fairness. The left exploits this inevitable ambiguity.
German has a seperate word "Justiz" for the legal system and uses "Gerechtigkeit" for what we call fairness in English.
The court(room) is interestingly "Gericht", which implies that this is a place where the law "Recht" is supposed to be administered fairly.
Note: do not worry about the pronunciation, just observe how the spelling indicates in which way the words relate or not.