The potential weak Hilbert property conjecture for special varieties

Let $K$ be a finitely generated field and let $X$ be a smooth projective variety over $K$. The variety $X$ has potential WHP if $X_L$ has the weak Hilbert property for some finite extension $L/K$. Potential weak Hilbert property conjecture. The following are equivalent:

$$\begin{array}{ll} \text{(i)} & X\text{ has potential WHP};\\ \text{(ii)} & \text{there is a finite field extension }L/K\text{ such that }X(L)\text{ is Zariski-dense in }X;\\ \text{(iii)} & X\text{ is special}. \end{array}$$

This combines the expected characterization of potential WHP by potential density with Campana's prediction that special varieties are the varieties with the opposing arithmetic behavior to varieties of general type.