Verbitsky's conjecture on exotic hypercomplex structures

A hypercomplex structure $(X,I,J,K)$ is exotic if $(X,I)$ is holomorphically symplectic, but for no choice of $\alpha \in \operatorname{Kahl}(X)$ does the corresponding hyperkähler structure equal $(X,I,J,K)$. Verbitsky's conjecture. Exotic hypercomplex structures do not exist. This claim concerns whether holomorphically symplectic hypercomplex manifolds can fail to arise from hyperkähler structures. The source presents it as a claim from Verbitsky and notes that the results proved there provide some evidence; its general status is not established in the supplied text.