The Puncturing Conjecture for potential density of integral points

Let $K$ be a number field, let $X$ be a smooth (quasi-)projective variety over $K$, and let $Z$ be a subvariety of codimension at least $2$. Assume that the rational points on $X$ are potentially dense. The Puncturing Conjecture. The integral points on $X\setminus Z$ should be potentially dense. This conjecture asks whether potential density of rational points persists after removing a subvariety of codimension at least $2$; the supplied text gives no resolution.