It was entirely possible they did have someone like Spider-Man in Caroline's world, but that Caroline herself was just not familiar. However, part of her did believe she had heard the name before. He was definitely the superhero sort then.
"We might? The name sounds familiar," Caroline replied. "But I'm not a big fan of comic books and I'm pretty sure that's where the familiarity comes from." She was pretty sure Elena's brother, Jeremy, was into those types of things. There were also more than a few people at the school that indulged in them from time to time (like MG).