Theoretically, sure it's falsifiable. Practically speaking, not really. Intelligence communities, not just of the US but also of any country, objectively have more capability to hide the truth than an average citizen has to expose it, especially when they have decades to have covered it up.

If I write a word on a piece of paper and then burn the paper, then I would have a belief about what was written on it, but that belief would not be practically falsifiable because no evidence exists to prove what was on it. Science cannot reconstruct everything that has ever happened everywhere.

The reason falsifiability is a standard in science is because science is concerned with making accurate predictions about the future. My broader theory is that the intelligence community was acting and continues to act according to it's own agenda, wielding significant power that isn't adequately checked by the civilian government. That's definitely falsifiable. I predict that first off, no president will act against the interests in a significant, meaningful way, and if they did, they would die, and high ranking members of the intelligence community would be placed on the investigative committee and find themselves innocent. If that didn't play out that way, it wouldn't definitively prove that that didn't happen with Kennedy because circumstances could have changed, but it would make it much less plausible (strict falsifiability isn't really how science generally operates, theories just become less likely until they're not worth considering).