The closest relevant legal precedent is the 2002 Beanie Baby decision by Judge Richard Posner (who has a taste for cases involving stuffed animals). Ty, the producer of Beanie Babies, doesn't like unauthorized guides to the Beanie Baby universe and their unflattering tendency to criticize the company, so it sued. Ruling against the company, Judge Posner used the same analogy that I have, comparing the guides to book reviews: "Both," he said, "are critical and evaluative as well as purely informational; and ownership of a copyright does not confer a legal right to control public evaluation of the copyrighted work." That's logic that should control the Potter case as well.
Even if the Beanie Baby case isn't directly controlling, the economics suggest the same result. How, exactly, are we hurt by the existence of competing guides to the Potter universe, one written by fans, the other by Rowling? It would be strange to say that since Fodor has written a perfectly good guide to London, we don't need the Lonely Planet or, for that matter, Wikitravel. Giving Rowling what she wants would be like giving Egypt the power to control guides to the pyramids.
Bizarrely, Rowling says that the fan guide would prevent her from writing her own guide to the Potter world. "I cannot," she said in a statement "approve of 'companion books' or 'encyclopedias' that seek to preempt my definitive Potter reference book. ..." To begin with, Rowling sounds entirely too much like a Death Eater in this quote. More generally, two products in the same market isn't called pre-emption—the word is competition. Why not let consumers decide which guide they like better? Rowling might object that the fan's guide will be strewn with errors or poorly written; but it is hardly the job of copyright to protect us from bad execution. And the fan's guide might actually be better, or at least different.
There are more ethereal reasons that Rowling ought not win. For reasons anthropologists will someday understand, volunteer encyclopedias have become the place to find what passes for our collective wisdom. Wikipediais the clearest example: It may be wrong sometimes, but it is nonetheless a statement as to what we know. To her credit, Rowling accepts this and tolerates the online version of the H.P. Lexicon. But a general rule of the kind she is asking for isn't so generous: It would, by necessity, give copyright owners power over the content of Wikipediaand other online encyclopedias that discuss their works. Not the end of the world, but certainly a subtle form of thought control.
In the end, this dispute is about the current meaning of authorship. Rowling is the initial author and deserves the bulk of the credit, respect, and financial reward. But she has all of that. What she wants is a level of control over the Potter world that just isn't healthy. The authors of fan guides, like house elves, rarely get famous or rich. They deserve legal credit for their modest contributions, not the Wizengamot.