Haines's refinement for triangles with sums of minuscule weights

Let $T=[x,y,z]$ be a geodesic triangle in a Euclidean building whose $\Delta$-side-lengths are $(\alpha,\beta,\gamma^*)$, where $\alpha$, $\beta$, and $\gamma$ are sums of minuscule weights. The theorem above assumes that one vertex of $T$ is special.

Haines's refinement. The assumption that one vertex of $T$ is special can be replaced by

$$\alpha+\beta+\gamma\in Q(R^\vee).$$

This refinement concerns the theorem asserting that $V_{\gamma}\subset V_{\alpha}\otimes V_{\beta}$ for such a triangle. The source attributes the statement to Tom Haines, but the supplied text gives no information about whether it has been proved or remains open.