Grinenko's rigidity conjecture for nonsingular dP3 fibrations

Let $X\to S$ be a $dP_3$ fibration with nonsingular total space. Say that $X$ satisfies condition $(\ast)$ when

$$-K_X\notin\operatorname{Int}\operatorname{\overline{NM}}^1(X).$$

Grinenko's dP3 rigidity conjecture. If $X$ satisfies condition $(\ast)$, then $X$ is birationally rigid. This conjecture extends the known rigidity theorem under the stronger $K^2$ condition to the condition $(\ast)$.