So the idea is that we have an AI whose utility function is constant on all possible worlds where JFK was assassinated. It therefore has no reason to care about what happens in those worlds and will try to optimize its behaviour for worlds where JFK wasn't assassinated. (And then, e.g., the point of this post is that given enough evidence for the assassination, it will be trying to optimize its behaviour for worlds that almost exactly resemble ones where JFK really was assassinated.)

If the AI thinks there's even a tiny chance that it can influence whether JFK was assassinated, it may be extraordinarily keen to do so. To put it differently, it may reason thus: "The versions of this world in which JFK wasn't assassinated are those in which either he never was but there's been a most extraordinarily effective conspiracy to make it look as if he was, or else he was but somehow that can be changed. The latter seems monstrously improbable because it requires weird physics, but at this point the former is also monstrously improbable; to maximize utility in JFK-unassassinated worlds I had better start looking for ways to make this one of them even if it isn't already."

(I think this is closely related to V_V's point.)