Even then many summary statistics rely on a well-defined PDF which is also not true for many real life cases. I think most data scientists out there are very familiar with quantiles, which are often more useful as all random variables have a CDF (and the quantile is just the inverse CDF).
I quite enjoy Taleb's writing (I tend to find his ego a bit amusing) but I think even he is guilty of Jaynes' "Mind Projection Fallacy"[0] in regards searching for more meaning than exists in Fat-tailed distributions. When we model our data with infinite/undefined mean and variance distributions we're just saying "I don't know". No amount of cleverness with summary statistics, or understanding of pathological distributions will create information where there is none.
The overall point being: there are many, many ways of viewing statistics and it's pretty trivial to find a perspective that allows you to call someone a "fraud". Sure there are actual frauds in data science, but one of the biggest strengths in this trend is bringing quantitative people from a wide range of backgrounds to gain refreshing insights. It is much more useful to encourage cross-discipline exploration than to simply say "you don't belong here".