Kninjanin, I was interested and watched the whole clip, because I only knew the succession as far as #3, the Speaker of the House.
That interesting discussion reminded me of May 30, 1981...it's one of those times you remember forever where you were, President Reagan was shot in an assassination attempt. But Alexander Haig, the Secretary of State, went on TV and announced something like “I, Al Haig, am in control here at the White House,” ...and for everybody not to worry.
That sounded like he was saying something very different than he actually intended -- either a putsch or else really unaware of the line of succession -- and he ended up getting phased out of the administration.
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Another memory of that time is that President Reagan was quite seriously wounded, but he never lost his famous sense of humour. As he was wheeled into the surgery, he said to the doctors attending him; "I hope you are Republicans."
And one of them had the compassion to respond, "We are all Republicans today."