Normal distribution, arrived at via the central limit theorem, assume that the underlying distributions are independent. They may well approximate independence most of the time, but when extreme events happen, the distributions are correlated, the CLT doesn't apply (not in the simple way it is normally presented), and the overall result is most definitely not normally distributed.

Normal distribution is a terrible model for estimating risk.

The quote isn't the first to confuse bad statistics with some inherent weakness in statistics. Black Swan was a worldwide bestseller based on the same canard.