When you decide that a value N standard deviations away from the mean is an anomaly that must be investigated, you implicitly make an assumption about the underlying distribution of the data.
Non-parametric means more than just avoiding talk of distributions.
In my previous post I said "doesn't assume any distribution" I meant it doesn't depend on any particular distribution function.
But in the post above that I was sloppy and said "no assumptions about the distribution at all". Good catch.
Instead, they determined N by looking at the past data.
(Contrast with the parametric approach of assuming normality and concluding that any point lying >3 sd from the mean is an anamoly due to properties of the gaussian distribution.)
Any tool can be used without regard for the consequences, but knowing a tool’s statistical properties yields know-how about the consequences of its application. It’s often a matter of the costs of error / stakes of the most problem at hand. Cheap solutions are often the best for cheap problems.