It's their point, and it's a good one, but I think they're somewhat overstating how common power-law data is; it probably varies a lot by field of study. And at least the logarithm of a power-law variable can help bring it back closer to the world of sanity. Plus, there are plenty of fields where nonparametric tests of medians are accepted standard practice.

You can turn most issues into powerlaws by recursing a reasonable risk distribution over it.

So suppose we ask, what is our confidence in X? (rather than X); and then, what is our confidence in the model by which we give confidences in X (ie., the model risk); and so on...

In practice, what we want to model is the appropriate confidence, not an actual prediction (bunk). So we are very often screwed.

Statistics is an illusion.