Politeness of coadjoint actions with locally closed orbits

Let $G$ be a Lie group with Lie algebra $\mathfrak{g}$, and let $G$ act on $\mathfrak{g}^{\ast}$ by the coadjoint action. Assume that every coadjoint orbit is locally closed in $\mathfrak{g}^{\ast}$. The coadjoint-action politeness conjecture. The coadjoint action of $G$ on $\mathfrak{g}^{\ast}$ is polite. This proposes a general criterion ensuring politeness of the coadjoint action; the supplied text gives examples supporting it but does not state a proof or resolution.