But John, surely there is no ideal legitimate authority - every national government is going to have some skeleton or other in its closet. Paul appears to have regarded Rome as a legitimate authority; but Rome was an idolatrous imperial power, established by force and invasion, which did not hesitate to intervene violently in the internal affairs of subject peoples (including Israel), which came to be perceived as a deeply anti-Christian power, and which ultimately came under divine judgment (Rev.18). It also seems to me that God can use the most unjust and illegitimate of nations to bring about his purposes if he wants to. What happens in the Bible, though, generally is that the unjust instrument of divine judgment also, sooner or later, finds itself judged.

By the way, it was Psalm 82:4 - maybe the author was using a Catholic Bible. The Psalm also has a universal perspective (verses 1 and 8) that may make it particularly relevant in the current circumstances, though usually these references to the poor and needy apply within the people of God.