Bang-Jensen et al.'s Meyniel-type conjecture for strong digraphs

Let $D$ be a strong digraph on $n$ vertices. For vertices $u,v$ of $D$, write $d(u)$ and $d(v)$ for their total degrees. Suppose that $u$ and $v$ are non-adjacent and have a common out-neighbour or a common in-neighbour.

Bang-Jensen et al.'s conjecture. If

$$d(u)+d(v)\ge 2n-1$$

for every such pair $u,v$, then $D$ is hamiltonian.

This conjecture is presented as a strengthening of the classical Meyniel theorem. Its resolution is not established in the supplied text.