If Obama is not responsible for killing Osama...

And by that same "logic" Truman was responsible for what happened at Hiroshima and Nagasaki.

It is a logical fallacy in every instance Raees. It would be correct to say that Obama participated in the act of killing Osama, to say that he authorized the mission certainly. But to say that Obama is responsible for the killing of Osama would mean that Truman was responsible for ending WWII.

Truman WAS responsible for dropping the atomic bombs.