So people lie about what they're wearing. So they lie about their gender. So they assume identifies different than their standard, non-cyber identities. So what. How many jokes can you make about that before the joke turns on itself. So many cartoons about the internet, for instance, have incorrectly constructed URLs in them, suggesting that the cartoonist knows close to nothing about what he or she is trying to make fun of.
But there's something about this one which either inadvertently and serendipitously, or perhaps intentionally, gets things right. The hero, after all, is being completely truthful in saying that he's wearing only a fur coat, but his assumption about who is on the other side of the line is totally off the mark. Yet that truthfulness beautifully corresponds to the hopes and expectations of the recipient. I like that.
But I doubt that a situation such as this would work in school.