Peter's position? Well, he's a superhero. I suppose that would map onto "aristocracy" in the real world in many ways. Alan Moore wanted to explore that comparison further in "Twilight of the Superheroes", with a new feudalism forming around the DC superheroes.
And even if Peter didn't enjoy a privileged upbringing, that doesn't magically erase any class subtext. His father-figure imprinted on him the idea that powerful people have a duty to others. When he ascended into the upper-class (so to speak), he had to relearn that lesson, brutally.