The coherence and sectional-curvature conjecture for Coxeter groups

Let $G$ be a Coxeter group with standard $2$-complex $X$, and let $\overline X$ be the compression of a finite cover of $X$ corresponding to a finite-index torsion-free subgroup. Say that $G$ has nonpositive planar sectional curvature when the relevant planar sections have nonpositive curvature. Coherence and sectional-curvature conjecture. If $G$ has nonpositive planar sectional curvature, then the following are equivalent:

1. $G$ is coherent.
2. $\overline X$ has nonpositive sectional curvature.

The preceding problem asks whether a positive-Euler-characteristic case is incoherent; an affirmative answer would support this broader proposed equivalence. The statement is not proved in the supplied text.