Generality conjecture for Fano 10-tuples of planes

Let $\underline{\Lambda}$ be a Fano $10$-tuple of planes in $\mathbb{P}^5$, and let the objects associated with it be as in Proposition cited in the source, including the EPW sextic, O'Grady's double cover, and its symplectic resolution. Generality conjecture. The assertions of the proposition hold for any Fano $10$-tuple of planes in $\mathbb{P}^5$, and not only for a generic one. The proposition's assertions concern the geometry of the associated double cover and symplectic resolution; the supplied text gives no evidence resolving whether they hold for every Fano $10$-tuple, so the conjecture remains open.