Sorry for being nit-picky. It is not that we evolved to thrive during periods of famine. It is that we did not evolve under conditions where resources were plentiful. That is why so many people die from heart conditions brought on by excessive eating. The machinery in our body is simply insufficient to deal with the excess cholesterol.
He's saying that even when people are universally weakened by starvation, the other mutations that exhibit advantages (a regenerative immune system in this case) are rewarded with further generations. I think "evolved to thrive in famine" is fair to say.