Russia’s President is elected by the people of Russia. He could be forced to resign so if there is any truth to the rumors - it would have been common knowledge in Moscow already, unless Kremlin factions can’t agree on a successor.
Khruschev lost the support of Communist Party elites because of his erratic policies and humiliating the Soviet Union during the Cuban missile crisis. He had no independent power base so his downfall was a foregone conclusion.
Putin may be sick or on vacation but a telling instance that he is still in charge is Rossiya Channel 1 tonight broadcasted an interview about his actions in Ukraine/Crimea. That would not have happened had he been deposed. Small things like this take on huge significance in Russia and for Western Kremlin watchers as well.
Very perceptive observation! Well done!!