Much of the work of these spooks, feds and snitches took place out of the public view.  However leadership changes in foreign governments and were seen by all, but without the understanding of what really happened.  Much of this clandestine work was done without the supervision of the executive branch or even the president and congress.  Budgets for these activities often showed up as some of the ridiculous projects like the study of transgender elephants in the heart of Africa.  Basically they were unsupervised and they pretty much ran their own foreign policy as was seen in Guatemala, Vietnam and, especially Cuba.  This is what led to the break down between the CIA and President Kennedy.  He fired the people at the top and was in the process of limiting their power when he died.  
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