Schoen's genus conjecture for index-one minimal surfaces

Let $M^3$ be a closed three-manifold with positive Ricci curvature, and let $\Sigma$ be an orientable minimal surface in $M^3$. Schoen's conjecture. If $\Sigma$ has index one, then

$$\operatorname{genus}(\Sigma)\leq 2.$$

The conjecture gives the expected sharp genus bound for index-one minimal surfaces in positively Ricci-curved three-manifolds. The paper's abstract says that the conjecture is confirmed for an infinite class of spherical space forms, while the supplied text does not state that it is solved in full generality.