A study to determine relative cognitive ability of children and grown-ups examines the relative levels of fantasy and reality that can be perceived. Many graphs and charts in the link, but the bottom line may be very bad indeed for Robin:
While kids and adults are largely in agreement about reality/fantasy and fantasy/fantasy, believing that Batman is make-believe and Batman believes SpongeBob is make-believe, there is a difference in the within-world responses. Kids are more likely than adults to say that Batman believes Robin is also a fictional character. Even for children, significantly fewer give this response than in the other conditions, but nonetheless, this study does reveal a striking difference between children and adults.
But do kids really believe that Batman doesn’t think Robin is real? That would make life in Gotham City rather perplexing, don’t you think? Why would Batman be motivated to fight crime at all, if he truly believed that all his adversaries were fantasies?
There is another possible explanation of the data: that children simply have trouble taking Batman’s perspective. Their answers might simply reflect their own knowledge that Batman’s world is fictional.