Graffiti's average-distance lower bound for the independence number

Let $G$ be a graph, let $\alpha(G)$ be its independence number, and let $\bar d$ be the average distance between distinct vertices of $G$. Graffiti's average-distance conjecture.

$$\alpha(G) \geq \bar d$$

The paper verifies this bound for several graph classes considered there, using $\bar d\leq 3\leq\alpha(G)$, but the conjecture is attributed to Graffiti and is not resolved in the source.