Well, until 1948 the Smithsonian claimed that Samuel Langley invented the airplane, so they're not infallible.
On the subject, it's difficult to prove authorship, particularly when the two were friends and worked together during the time of authorship. My gut feeling is this:
The book is Lee's work. Capote was likely a sounding board, but in essence, it is Lee's. Capote's In Cold Blood was an excellent book, but it never got the literary acclaim that Lee's book got. As Capote got older, drank more, and became more and more of a joke, I think he wanted to claim some of the adulation. With the possible exception of Breakfast at Tiffany's, most people probably couldn't name a Capote novel except In Cold Blood. For an attention hound like Capote, it must have been galling that his former assistant wrote one book that was considered far more of a classic than anything he ever wrote, and I think he might have been desperate enough to try to grab onto some of that fame.
Posts #49, 76, & 78 take all the mystery out of who wrote what. It’s no secret.