I'm not so well versed in Chinese history myself, but I believe this narrative. One thing that confirms this is a graph of China's population. It shoots up after 1950, and you can't really identify either of these major catastrophes by looking at a population graph. The obvious explanation is the population shot up because people had enough to eat, notwithstanding these two discrete events.
Would Chiang Kai-shek have done better? The Guomindang certainly wanted to institute land reforms that would have benefited peasants (the vast majority of Chinese) without the central control of communism. On the other hand, it's not clear that the Guomindang would have had the power to actually implement these policies.