The explanation I’ve heard that makes the most sense to me is that Lenin’s wife preferred Trotsky to Stalin and essentially fabricated the idea that Lenin did as well shortly before and after his death. She (understandably) spent the most time with him and could claim he had said or written just about anything during a lucid moment. And the details may not even be falsified, just reported through a biased filter - criticism of Stalin emphasized, criticism of Trotsky ommitted or downplayed.