No, there's a significant difference between "prove something happened" and "prove something didn't happen". If there's a document in there detailing a conspiracy by the CIA to kill JFK, and it gets released someday, a lot of people are going to be convinced. It's less true in the other direction.
I guess I don't understand your distinction here on purely logical terms, why the uneven burden of proof? The Warren Report is just that, a report written by humans. Even if you firmly want to believe it, if you read it you'd understand its not really doing anything differently than the tin-foil heads and their books (of the better ones at least). It did not create the reality of its hypothesis along with it, it can't really know what Oswald was thinking.
Have you seen the documents they released in the past? There are so many redactions. They are undoubtedly hiding something deemed too sensitive for the public.