DeMarco's orbit-closure conjecture for pairs of marked points

Let $f_t(x)$ be a non-isotrivial algebraic family of rational functions of degree greater than $1$ over $\mathbb C$, parametrized by $t\in\mathbb A^1_{\mathbb C}$, and let $a(t),b(t)$ be marked points defined over $\overline{\mathbb C(t)}$. DeMarco's orbit-closure conjecture. If there are infinitely many $t_0\in\mathbb A^1$ such that $a(t_0),b(t_0)\in\operatorname{Prep}(f_{t_0})$, then

$$\overline{\operatorname{Orb}_{(f_t,f_t)}((a(t),b(t)))}\subseteq(\mathbb P^1\times\mathbb P^1)(\overline{\mathbb C(t)})$$

is a proper Zariski-closed subset. This is a special case of the conjecture explicitly stated in DeMarco (2016), concerning unlikely intersections and simultaneous preperiodicity in algebraic families; it is not resolved in the source.