The real Schur-element ratio conjecture for blocks

Let $W$ be a complex reflection group, let $\theta:q\mapsto\xi$ be a specialization of ${\mathcal H}_q(W)$, and let $s_\chi$ denote the Schur element associated with $\chi\in\operatorname{Irr}(W)$. If $\chi,\psi\in\operatorname{Irr}(W)$ belong to the same block, the Schur-element ratio conjecture asserts that

$$\theta\left(\frac{s_\chi}{s_\psi}\right)\in\mathbb{R}^{\times}.$$

The paper reports that this holds in all of its examples, and notes that the ratio is in fact in $\mathbb{Q}^{\times}$ there; no general proof or refutation is supplied in the given text.