Campana's specialness and potential-density conjecture

Let $X$ be a variety over a number field $K$. The set of integral points on $X$ is potentially dense if it becomes dense after a finite extension of $K$ and a suitable choice of finitely many places and model.

Campana's conjecture. $X$ is special if and only if the set of integral points on $X$ is potentially dense.

This conjecture relates Campana's geometric notion of specialness to arithmetic density. The source states it as a further conjecture but gives no resolution.