Cameron–Lucchini–Roney-Dougal's conjecture on the generating graph and replacement number

Let $G$ be a finite group. The generating graph $\Gamma(G)$ has vertex set $G$, with two distinct vertices adjacent when they generate $G$. A vertex is isolated if it has no adjacent vertex. The replacement number $\psi(G)$ is the smallest value of $r$ for which the equivalence relations $\equiv_m$ and $\equiv_m^{(r)}$ coincide, where $x_m y$ means that $x$ and $y$ can be substituted for one another in all generating sets for $G$, and $x_m^{(r)}y$ means that they can be substituted for one another in all generating sets of size $r$. Cameron–Lucchini–Roney-Dougal's conjecture. If no vertex of $\Gamma(G)$ is isolated, then $\psi(G)\leq 2$. The conjecture asserts that the absence of isolated vertices forces the equivalence relation determined by all generating sets to coincide with that determined by generating sets of size at most two. Its resolution is not established by the supplied text.