You're right. It's much more likely that is was a massive conspiracy requiring the involvement and complicity of hundreds - if not thousands - of people from inception to planning to execution, none of whom have so much as spilled the beans about it. Because gawd knows, if anyone can pull of such a complicated plot and subterfuge it's a government - they never fuck anything up.
And they would've gotten away with it to but for internet sluthes and their not at all contradictory explanations and theories.