The conjecture on type I groups acting on trees

Let $T$ be a thick tree, and let $G \leq \operatorname{Aut}(T)$ be a closed subgroup. A compact open subgroup of $G$ is assumed to act transitively on the boundary $\partial T$.

Type I conjecture. Under these assumptions, $G$ is a type I group.

The paper presents this as a conjecture motivated by its non-type-I result for certain groups acting on trees. No resolution is given in the source, so the conjecture remains open.