I think Mayson's labeling Superman as a vigilante had less to do with his powers and more with his anonymity. Can there be due process when the person making the citizen's arrest is anonymous?
Superman isn't anonymous. He's Superman from the planet Krypton. It's not the same situation as, say, Batman. Batman is obviously someone else who is hiding his identity and could reasonably be considered anonymous. Superman is not known to have a secret identity, so there's no reason to believe that he's someone unknown hiding his identity.