Where the "conspiracy" portion enters in, is over who the group was, what their purpose was for doing so, and how effective they've been/will be in pulling it off (assuming they're the ones that managed it, and not one of the other conspiratorial groups floating around out there).
Conspiracy fact--sure.
Conspiracy theory--no. Not theory. Far too much evidence for theory, in my case--had to work with toooooo many documents from the puppet masters' own publications.