Not a conspiracy theory, per se, but even though flawed, a chain of deduction.
That is, if you had been in a position of power at the time, and had this chain of deduction pointed out to you, how would you have grasped it? In summary:
1) The president has a severe disease, and the only drug he can take for it may be making him paranoid, psychotic, and homicidal.
2) The US has just been through a major crisis, in which either the president, or the USSR, could have started a nuclear war, and came very close to doing so.
3) The president refuses to leave office voluntarily.
Is there any possibility that given this information, you would agree that the president must be removed from office before he could start a war?