Conjecture on homogeneous products of faithful irreducible characters

Let $G$ be a solvable group, and let $\psi,\varphi\in\operatorname{Irr}(G)$ be faithful, where $\operatorname{Irr}(G)$ denotes the irreducible characters of $G$. Suppose that

$$\psi\varphi=m\chi,$$

where $m$ is a positive integer and $\chi\in\operatorname{Irr}(G)$. Homogeneous-product conjecture. Then $\psi$ and $\varphi$ are fully ramified with respect to $\mathbf{Z}(G)$, the center of $G$. This conjecture generalizes Isaacs's conjecture about irreducible products of faithful characters; the source gives no resolution status.