Thank you for this terrific answer. Yikes, JFK admits that "we suggested the coup". Not good for him.
Let us hope that he was more of a passive than active part of the "we," but even then "We got a problem Houston." At least JFK wasn't pressured into tossing ground troops into Vietnam (there were some 16,000 American advisors there at the time of this death). Perhaps, he had thought about General MacArthur's sage advice: ""Never get involved in a land war in Asia." (He greatly admired MacArthur who was his top military commander in the Pacific Theater in WWII and who later came to visit him in the White House as seen in the below video.)
Secret JFK/MacArthur White House conversation (I love it how MacArthur slams Eisenhower): https://archive.org/details/jfk_012