Polynomial convexity of totally real discs in singular Levi-flat hypersurfaces

Let $K$ be a totally real disc lying in a singular Levi-flat hypersurface in $\mathbb{C}^2$, and let $\widehat{K}$ denote its polynomial hull. The singular set is the set of singular points of the hypersurface.

Second conjecture. The disc $K$ is polynomially convex if

$$\widehat{K}\cap\operatorname{Sing}(M)=\varnothing,$$

where $M$ is the singular Levi-flat hypersurface containing $K$.

This conjecture is motivated by the paper's results on Levi-flat quadrics and their normal forms, together with the condition that the polynomial hull avoid the singular set. Its status is not resolved in the supplied text.