Let $I$ be a radical ideal of a regular local ring $S$. Put $R:=S/I$. Let $I^{(n)}$ be the $n$-th [symbolic power](https://en.m.wikipedia.org/wiki/Symbolic_power_of_an_ideal) of $I$. It is well-known that $I^n \subseteq I^{(n)}$.

 Is it true that $I/I^2$ is $R$-free if and only if $I/I^{(2)}$ is $R$-free?