"El auto se rompió" IS passive voice Gabriel. That's for sure. "se" for passive voice is as much used as the other passive, sometimes it depends on the sentence, for isntance, "el auto fue roto" sounds so bad it's hardly ever heard, never I'd say.
Now, taking into consideration this sentence is a passive voice, when you analyse it you have "el auto" is the subject of the sentence, so you were right. IT IS the subject of the passive.
Who broke the car? How did it happen? Why it broke down? Nobody cares. That's why the passive voice is used in this sentence, because what just matters is that "el auto se rompió" (and you have to walk
-just kidding)
Hope it helps!