There's no way (for most of us with finite resources) to verify the vast majority of history, even recent history, even history that happened today. To me this is like saying "who cares what may or may not have happened in the past".
This particular conspiracy theory is interesting because the assumed enemy here—the Soviet Union—was ostensibly (and seeming authentically) unhappy to see this happen. So who wanted JFK dead and why?
Sure, it's the obsessing over conspiracy theories that I don't get. There's no way to verify the various speculations, so what's the point?