Kuznetsov–Polishchuk fullness conjecture for isotropic Grassmannians

Let $V$ be a $2n$-dimensional symplectic vector space, let ${\mathsf{IGr}}(k,V)$ be the isotropic Grassmannian, and let ${\mathcal{A}}_t$ be the admissible subcategories defined by the Kuznetsov–Polishchuk exceptional blocks. Theorem~9.2 gives semiorthogonal subcategories

$${\mathcal{A}}_0,\ {\mathcal{A}}_1(1),\ldots,{\mathcal{A}}_{2n-k}(2n-k)$$

and hence an exceptional collection of length $2^k\binom{n}{k}$ in $D({\mathsf{IGr}}(k,V))$. Kuznetsov–Polishchuk's fullness conjecture. The exceptional collections in Theorem~9.2 are full, i.e. they generate $D({\mathsf{IGr}}(k,V))$. The collection has the expected length, equal to $\mathop{\mathsf{rk}} K_0({\mathsf{IGr}}(k,V))$, so fullness would provide a complete exceptional collection for the isotropic Grassmannian. The supplied text does not indicate whether this assertion has been proved or disproved.