Who shot JFK?

For the purposes of this post, I don't really care who shot JFK; it's just a convenient mystery with which I can ask a question about truth.

Alice believes that Lee Harvey Oswald shot JFK. She believes that Lee Harvey Oswald was in the Texas Book Depository, aimed a loaded rifle and shot JFK, at which point his head visibly exploded as seen in the Zapruder video.

Bert disagrees; he doesn't know for sure who shot JFK, but the one thing he's sure of is that Lee Harvey Oswald was not pointing a loaded rifle out of the window of the Texas Book Depository at the President at the fateful moment.

What do I believe? As I say, I neither know nor care, but there's one thing I know for sure: one of Alice or Bert is wrong. In sufficiently weird conditions both of them might be wrong, but one of them is wrong for sure. We may never know which of them is wrong, but at least one of them is definitely wrong.

Does anyone disagree with this?

Truth, strike two

Thanks for some interesting and surprising responses to the JFK question. At the risk of creating more heat than light, let me try another example, one that I think might be a little less comfortable to be neutral about.

It seems that many people believe that on the morning of September 11, 2001, four thousand or more Israelis who were working at the World Trade Center did not show up for work.

Are those people wrong?

(Update: amended as per ajva's caveat)