He turns at the exact moment JFK receives the crucial head shot. The direction of the shot would be correct as to JFKs body movement and blood splatter on impact, and a close range 45 handgun would do that amount of damage. Also, eyewitnesses saw "fireworks" in JFK's limo.
I'm not much of a conspiracy theorist, but in JFK's case I can't buy just Oswald.
Anyway, feel free to add your own theories.
I think LBJ was likely complicit.