Kennedy said he wanted to "splinter the C.I.A. in a thousand pieces and scatter it to the winds."
It was allegedly made to someone in his administration, uncertain when.
JFK {it is thought} ran into the establishment in the form of CIA Director Allen Dulles {WWII: OSS} and his brother John Foster Dulles {Prez. Eisenhower's Sec of State}. Allen D apparently tried to foil JFK at Bay of Pigs despite the Prez calling off air cover... also CIA ran 'Black Ops' at the time, or 'Wet Ops' some might have called it.
JFK is a truly fertile field for speculators and conspiracy theorists.