The maximal non-Gorenstein locus characterization for Schubert varieties

Let $X_w$ be a Schubert variety, and let $X_v$ range over the Schubert varieties contained in its maximal singular locus. The maximal non-Gorenstein locus characterization proposes that the maximal non-Gorenstein locus of $X_w$ is the union of those Schubert varieties $X_v$ for which the generic point is not Gorenstein in $X_w$.