Rigidity conjecture for nonnegative Q-curvature on closed flat manifolds

Let $n\geq 3$, and let $(M^n,\bar{g})$ be a connected closed flat Riemannian manifold. A metric has pointwise positive Q-curvature if its Q-curvature is positive at every point. Rigidity conjecture. There is no metric on $M$ with pointwise positive Q-curvature. Moreover, if a metric $g$ on $M$ satisfies

$$Q_g\geq 0,$$

then $g$ is flat. This would extend the preceding rigidity results for flat tori to all closed flat manifolds, using the Bieberbach theorem; the source does not provide a resolution.