I would expect the argument to grow closer to one of their Vigilante nature rather than fascist.
There is a clearer argument that they do what they do because they feel they fill a void in the justice system. They lack a full faith in the system to some extent. If they were deputized they would be required to follow the rules of those we put in charge of our system and they would become a part of the system. The fact that they mostly work outside and around that system suggests that they don't want to be hampered by the system and once again we circle to the lack of faith in the system.
I suppose from there if they were organized by someone with an agenda who became their moral compass, then there might be a reason to begin to believe there could become an element of fascism in the whole picture.
But it feels more like those who suggest the fascism are pointing at the creators of the characters as the ones acting as the moral compass and perhaps capable of misusing that. This may be part of the reason the Comic Code Authority existed for a period of time, to help regulate those creators from doing just that. The problem with that type of regulating is that eventually you would have to move on to movies and books and that begins to sound pretty fascist to me.
It's a conundrum wrapped in a riddle.
