President Clinton, writing in the New York Times, reviewing Robert Caro's The Passage of Power, says:
Caro paints a vivid picture of L.B.J.'s misery. We can feel Johnson's ambition ebb, and believe with him that his political life was over, as he was shut out of meetings, unwelcome on Air Force One, mistrusted and despised by Robert Kennedy.
This "unwelcome on Air Force One" theme says more about Johnson's ego and insecurity than it does about President Kennedy's treatment of him. President Kennedy's position — as Caro mentions at one point in the book, though not when he first brings up the Air Force One issue at the beginning — was that it was a bad idea to have the president and the vice president both on the same plane, because if the plane crashed, or was shot down, or was out of communications contact, then the American government would be without both a president and a vice president. It was a simple national security, command and control, and continuity of government issue, not any snub of Johnson. I know of parents who, for somewhat similar reasons, don't fly on the same plane if they are traveling together apart from their young children. An excess of caution, perhaps, but there it is.