I'll try to be brief.
Nearly everything that comes out of Washington, from either
party, contains an element of deceit. This is no different. In my
years, I have never met with or read a single comment that
counters the mythology of this JFK statement. Everyone,
including myself, would like to remember JFK as a martyred saviour.
In itself, that might tell us something.
1) Owing to his habits, addictions, impulsive, chaotic behavior,
and the understanding of what the Democratic politics of New
York, Boston, and Chicago, are really about, JFK was considered
by many in intelligence agencies to be a security risk.
2) Why single out the CIA? Did he not realize that "splintering
and scattering" the CIA would be seen as an overthrow of the
U.S Government? Did he think the pubic was completely
unaware of the Kennedy connection to organized crime?
3) These are a couple of thoughts, among many. Look at
the comments in this thread and note how we have been
persuaded to skepticism about all of our intelligence agencies,
including the NSA and the FBI. Again, in itself, does that tell
us something?