It's one of those things I don't trust the government on,

So one of those everything?

Cause the government is not to be trusted. However, there is no strong historical evidence saying anything other than what I just specified.

as we are talking about a war where the British used a dead body to trick the German's on a fake invasion route.

That's just ordinary. To be able to keep it secret for 80 years afterwards would take superhuman ability, particularly when people have been asking questions about it.

I think the fact the Soviets were panicking around even asking their intelligence service 'this wasn't us right?' To which their response was 'we know the shooter, but too unstable to use so avoided him' makes me think the CIA knew he had brief contact and thought 2 birds, 1 stone as JFK was a thorn in their side.

I'm not so sure. Considering that I don't like the CIA, it'll be very tempting to just say yes, so I'll have an argument against them - but I just haven't seen the evidence.

And to be fair, if they were involved, obviously they would do their best to hide the evidence. Which they do. But there can be other reasons why they try to hide the evidence.