The characterization of rings with strong avoidance

Let $R$ be a commutative ring. Say that $R$ has strong avoidance if every pair of ideals of $R$ whose union is $R$ has one ideal equal to $R$. For each prime ideal $\mathfrak{p}$ of $R$, let $R_{\mathfrak{p}}$ denote the localization of $R$ at $R\setminus\mathfrak{p}$. Strong-avoidance characterization. A ring $R$ has strong avoidance if and only if, for each prime ideal $\mathfrak{p}$ of $R$, the ring $R_{\mathfrak{p}}$ is a principal ideal domain.

This problem asks for a local characterization of the strong avoidance property in terms of the structure of all prime localizations. The supplied text does not indicate whether the characterization is known or remains open.