siunitx syntax issue "\," versus "," for thousands separator

Question

This question includes a solution but I really want to know why it works and why what "should" work doesn't I think my MWE says is all:

\documentclass[12pt]{article}
\usepackage{siunitx}
% TeX Live 2015 (Ubuntu 18.04)
% siunitx Ver 2.6m
\sisetup{
group-digits=integer,
group-minimum-digits={3},
group-separator={,} % NOT "\,"
}

\begin{document}

After  looking at a number of examples (and the
documentation) I could not got what I wanted
(3,000). If group-separator is set to \verb:{\,}: 
the thousands separator is a space. But if set to
"," it works.

\begin{tabular}{ccc}
Code in document    &              & Typeset as\\
\hline
\verb:\num{3000}:    &  \num{3000}  & 3,000\\
\verb:$\num{3000}$:  & $\num{3000}$ & 3,000\\
\verb:\num{$3000$}:  & does not work\\
\end{tabular}
\end{document}

Answer 1

The token \, is not an “escaped comma”, but a command on its own, which means “insert a thin space (one sixth of an em). With

group-separator={whatever}

the separation between groups is set to whatever. Thus with

group-separator={,}

you'll get a comma, but with

group-separator={\,}

you'll get a thin space.

The braces are only mandatory with the comma, otherwise the option parser would get confused.