Exactly, it’s a smuggled assumption. A standard deviation is the second moment of a normal distribution. A negative binomial is a much better model for count data: https://statwonk.com/poisson-gamma-negative-binomial.html
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.