The type I conjecture for boundary-transitive groups acting on trees

Let $T$) be a locally finite tree, and let $G$ be a closed subgroup of ${\mathrm{Aut}}(T)$ acting transitively on the boundary $\partial T$.

Type I conjecture. Then $G$ is a type ${\rm I}$ group.

This conjecture asks for a characterization of type ${\rm I}$ closed subgroups of automorphism groups of trees. The paper studies this problem and proves broad non-type-I and non-amenability results, but the supplied text does not establish the conjecture in full.