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Actually she does own the character, doesn't she? I would assume so, since HP is her creative property.
At the same time though I cannot see how a reference guide to her works, even in bookform, would be theft. It sounds more like it would be a helpful source for scholarly and educational research. This guy is not claiming that he created the characters, allusions, etc, but rather that he is trying to put them in an organized, easily accessible fashion.
It bothers me that Rowling is so bothered by this.