Special-leaf correspondence for Coulomb and Higgs branches

Let $G$ be a reductive group, let $\mathbf{N}$ be a representation, and let $\mathcal{M}(G,\mathbf{N})$ and $\mathcal{M}_{\mathsf{Higgs}}(G,\mathbf{N})$ denote the associated Coulomb and Higgs branches. Let $\operatorname{CH}\subset \operatorname{Leaf}(\mathcal{M}(G,\mathbf{N}))\times\operatorname{Leaf}(\mathcal{M}_{\mathsf{Higgs}}(G,\mathbf{N}))$ be the correspondence defined by the maximal-torus data, and call a flat good when it has the property used in the definition of special leaves. Special-leaf correspondence conjecture. The special leaves of $\mathcal{M}(G,\mathbf{N})$ are precisely those whose image under $\varrho$ is a good flat. The relation $\operatorname{CH}$ gives a bijection between the special leaves of $\mathcal{M}(G,\mathbf{N})$ and the special leaves of $\mathcal{M}_{\mathsf{Higgs}}(G,\mathbf{N})$. This would identify the distinguished leaves on the Coulomb and Higgs sides, resolving the possible failures of the full leaf correspondence to be bijective; the source presents it as an alternate definition and does not state a resolution.