The Torelli group commuting-or-free conjecture

Let $S$ be a closed surface, and let $\I(S)$ denote the Torelli subgroup of the mapping class group, consisting of mapping classes acting trivially on $H_1(S,\mathbb{Z})$. Let $g,h\in\I(S)$.

Torelli group commuting-or-free conjecture. Either $g$ and $h$ commute, or the subgroup they generate is a free group:

$$\langle g,h\rangle \text{ is free}.$$

This asks whether every two-generator subgroup of a Torelli group is either abelian in the pairwise commuting case or free. The supplied text does not state whether the conjecture is known or remains open.