The discriminant-complement identification with the two-component link complement

Let $V_2$ be the two-dimensional complex Cartan subalgebra for the Lie algebra of type $G_2$, and let $V_2^{\rm reg}$ be the complement of the six root-kernel lines. Let $W_{G_2}$ act on $V_2^{\rm reg}$, and let $\mathbb R_+^*$ act by dilations; these actions commute. Write $L$ for the two-component link appearing in the modular-orbifold description of the cluster ${\cal X}$-variety associated to ${\rm Conf}_3({\cal B}_{G_2})$. Discriminant-complement conjecture. The quotient $V_2^{\rm reg}/\mathbb R_+^*W_{G_2}$ is homeomorphic to $S^3-L$. The identification would relate the quotient of the regular Cartan complement for the Coxeter group of type $G_2$ to the link complement already arising from the cluster ${\cal X}$-variety. The source gives no resolution status for this claim.