Arthur-type uniqueness conjecture for smooth orbit closures

Let $G$ be a classical group over a $p$-adic field $F$, let $\lambda$ be an infinitesimal parameter, and let $C$ be an orbit in the Vogan variety $V_\lambda$ whose closure $\overline{C}$ is smooth. Let $\mathcal{L}$ be a local system on $\overline{C}$, and set $\pi=\pi(C,\mathcal{L}|_C)$. Arthur-type uniqueness conjecture. If $\pi$ is of Arthur type, then the associated parameter $\phi_C$ is of Arthur type and there is a unique Arthur parameter $\psi$ with $\phi_C=\phi_\psi$, namely

$$\Psi(\pi)=\\{\psi\\}.$$

In particular, when $\pi=\pi(C,\mathbf{1})$ is of Arthur type, $\phi_C=\phi_\psi$ for some Arthur parameter $\psi$ and $\Psi(\pi)=\\{\psi\\}$. The claim is presented as a consequence of the cited conjectural identification of ABV- and Arthur packets.