There are two points here.
First, I agree that as a piece of cinema, JFK is absolutely riveting. Brilliantly written, directed, edited, acted, and with a great music score by John Williams. It's a stirring and powerful film I've returned to again and again.
Secondly, the history: My personal opinion is that something is indeed rotten in Denmark with the Warren Commission (and therefore, by definition, there is some kind of conspiracy). However, I do think Oliver Stone is a firm believer in the old adage that one should never let facts get in the way of a damn good film. There is much here that has been soundly debunked, and one should never mistake this film for a history lesson.
On that note, when I first saw this film with my father (in early 1992), afterwards, as we left the cinema, I asked him: "How were you involved in the Kennedy conspiracy? Oliver Stone has implicated everyone alive in 1963, so what was your role?"