Grove–Wilking–Yeager problem on hyperbolic orbit spaces and rational hyperbolicity

Let $M$ be a compact, simply connected manifold with an isometric action by a compact group $G$. The orbit space $M/G$ is assumed to have dimension two and to be covered by the hyperbolic plane. Grove–Wilking–Yeager problem. Under these assumptions, $M$ is rationally hyperbolic. This is a proposed sharp counterpart to the criterion that elliptic two-dimensional orbit spaces imply rational ellipticity; the source does not state whether the problem has been resolved.