But what would be wrong with doing that? Actually the idea is kind of interesting. That's one of the uses of fiction it seems to me - to play around with ideas, sort of ask "what if?". So what if it's not true? That's why they call it fiction.
Would you have a problem with it if Vidal said, "This book is a work of fiction, but the theory about Abraham Lincoln being the composer of Beethoven's works and about him being married to Julia Roberts is based on solid historical evidence."
That's what Brown is saying with DiVinci Code. No one is saying that he's denying it's a fictional book. What a lot of people are choking on is the fact that he's saying it's a fictional book that based on solid historical theory. The ideas in his book about Christ have been examined for years and have been found wanting.
Peter Shaffer's play Amadeus and its film adaptation by Milos Forman were similar exercises which played with ideas based on limited historical knowledge. If you had been there, in Mozart's time, you'd know they got it all wrong, but none of us had.
Fiction, even fiction that "plays with ideas" starts out by observing history and then filling in the author's ideas. But twisting historical events and the nature of organizations that are still with us? Opus Dei a buncha murderous thugs? No thanks, Danny boy.
Those are interesting questions outside of this discussion and they're covered in a thin book by Umberto Eco Six Walks in Fictional Woods, which is a collection of his university lectures, I think. Highly recommended.