Another thing silly about this idea is, suppose that Eisenhower and Nixon did start some sort of conspiracy. It does not seem reasonable that Kennedy and Johnson would just continue it (disagreements between Democrats and Republicans was not invented within the last 5 years
). Similarly, if it started under Kennedy and Johnson, it doesn't make sense that Nixon would just allow it to continue - it would have been a great way to destroy his opposition!
And I'm not taking a political side on either side - I'm just commenting on the nature of the beast of politics.