The non-virtual-regularity conjecture for scale group actions

Let $G$ be a compactly generated, topologically simple totally disconnected locally compact group, let $x\in G$ satisfy $s(x^{-1})>1$, and let $V_{--}\rtimes\langle x\rangle$ be the associated scale group acting on the boundary of the tree $T_{s(x^{-1})+1}$, with distinguished end $\omega$. Non-virtual-regularity conjecture. The action of $V_{--}\rtimes\langle x\rangle$ on

$$\partial T_{s(x^{-1})+1}\setminus\{\omega\}$$

is not virtually regular. This is presented as a companion to a criterion concerning two-transitive actions on tree boundaries. The paper states that the conjecture says nothing about compactly generated, topologically simple uniscalar groups, and its status is not resolved in the supplied text.