An unfortunate counterpoint to that is the number of Soviet wartime atrocities such as the Katyn Massacre that the Soviets blamed on Nazis by virtue of the Nazis falling into the trap of open, flamboyant brutality where the Soviet dictatorship, the professionals in the game, did all that in secret and took secrecy to an art form. The Soviets covered all that up for decades and there were plenty of people in the Cold War who sincerely believed that Nazis, not Soviets, perpetrated Katyn and to claim otherwise was a sign of sympathizing with Nazis. And of course mentioning this in the USSR got you either shot by the NKVD/KGB or exiled to Siberia.

The Nazis indisputably did fail with their atrocities, the Soviets did with theirs. Of course the Bush Administration was incompetent and amateurish. It did engage in that kind of reality-censorship, particularly where science was concerned, but this was known if not a common topic of discussion. The degree to which it was known indicates strongly that the Bush Administration would never have kept that secret.

Besides, as a Yank m'self it doesn't take much to get the USA involved in wars like that, the conspiracies are unnecessary.