Non-positive irreducible curvature implies coherence

Let $X$ be a finite, standard, irreducible 2-complex, and let $\rho_+(X)$ denote its positive irreducible curvature invariant.

Non-positive irreducible curvature implies coherence. If $\rho_+(X)\leq 0$ then $\pi_1(X)$ is coherent.

This sharpens Wise's coherence conjecture for non-positive immersions. The source gives no resolution, although it identifies the claim as a stronger conjectural consequence of non-positive irreducible curvature.