I'm currently watching the Ken Burns Vietnam War series and there were some pretty damning things said behind closed doors between Kennedy and McNamara, Johnson and McNamara, and Nixon and Kissinger, etc. that reveal their private doubts about the war, political motivations to prolong the war, etc. that really put them in a pretty bad light at times. I can't imagine they would have said some of the things they did if they knew it might get out somehow at a later time?
Lyndon Johnson intentionally recorded most of his phone calls and some of his cabinet meetings for historical posterity, and as they were considered his private documents rather than government records, he figured they would be released to the public when he wanted them to be released, long after it mattered to him. As he approached the end of his term, he was getting more selective of what he recorded.
Nixon went even further and had a full recording system built into the Oval Office. He wanted to be able to re-listen to whole conversations, as he intended to use the tapes to help write his memoirs once he retired. He was fully aware that everything said in the Oval Office was being recorded, but most of his staff did not. When Watergate came around, Nixon tried and failed to use the shield of 'executive privilege' to prevent the tapes from being used as admissible evidence, once the Special Prosecutor, Archibald Cox, figured out that these tapes existed.
To my knowledge, most of the Kennedy phone conversations involving Johnson were recorded by Johnson (not Kennedy), and Kennedy may not have been aware of them, though Kennedy would likely have known of any Oval Office or cabinet meeting recordings.