Butler et al.'s complement coalescing conjecture for distance matrices

Let $G_1$ and $G_2$ be graphs with $B_1\subseteq V(G_1)$ and $B_2\subseteq V(G_2)$. Coalescing conjecture. If coalescing the same connected rooted graph onto every vertex of $B_1$ and $B_2$ always produces cospectral pairs for the distance matrix, then coalescing the same connected rooted graph onto every vertex of $V(G_1)\setminus B_1$ and $V(G_2)\setminus B_2$ should also always produce cospectral pairs for the distance matrix. This conjecture concerns whether a universal coalescing construction for specified vertex sets is preserved when those sets are replaced by their complements; the paper states that it answers the conjecture negatively.