Richard Nixon actually said...
But getting rid of Castro in Cuba would not get rid of Castroism in Cuba or in Latin America and it would set in motion, in my opinion, a chain reaction of opposition to the United States through the other Latin American countries, which could be very, very detrimental to our foreign policy.
Context
Press Conference of Vice President Richard M. Nixon, Kentwood Arms Hotel, Springfield, MO
09/20/1960