Guo–Tointon conjecture on uniformly controlled coset spaces

Let $G$ be a finitely generated residually finite group. The group $G$ has the uniformly controlled (u.c.) property if its finite-index subgroups have uniformly almost flat coset spaces, as defined in the paper.

Guo–Tointon conjecture. $G$ has the u.c. property if and only if it is virtually nilpotent.

This is a partial statement of the conjecture on coset spaces proposed by Guo and Tointon. The supplied passage does not state whether the conjecture is resolved in general.