There have been arguments that certain things took place because of a fear for public demand for war if there was foreign involvement in the JFK assassination. There's even quotes from LBJ substantiating the idea itself, but I'm not buying it. Public opinion never has had its finger on the red button. Nuclear release has always been the prerogative of the president and LBJ's "40 million people" comment was bunk. I'm also inclined to believe that the public wouldn't be very anxious to participate in a 'guaranteed mutual destruction' event. I also don't believe that if LBJ or any other government official was convinced that there was foreign involvement in a presidential assassination that they would just sweep it under the carpet with Oswald's death. It would be investigated ruthlessly, because they wouldn't want the world to see how easy it was to off a president. Especially for a turd like LBJ. His actions in the subsequent months were very telling of his role in some really evil doings.
The public may not have its hand on the "nuclear football,"but they do have it on the handle of the voting machine. If word got out that JFK was killed by a Cuban hit team (even without mention of the assist from Bulgarians working for the KGB) they would fully expect that the US send the Marines to teach Fidel a lesson. Any President would run the risk of not being re-elected. After the Cuban Missile Crisis, it was hard to judge how the Kremlin would react, but they might be inclined to escalate in the face of what they perceived as Khrushchev 's earlier "weakness." It would be more palatable from the government's point of view that the American people believe that the President was killed by an unhinged loner exercising his Second Amendment rights than admit that foreign agents were operating lethally,and with compete impunity, in the United States. In order to tease out the details of the plot, they would need Oswald alive on the one hand, while leaving the foreign operatives convinced that they were in no danger from the information in Oswald's head. As I have said, this is one of the few odd aspects of the affair that makes any sense.