Donagi's small Schottky–Jung locus conjecture

Let $J_g$ be the Jacobian locus in $\mathcal A_g$, and let $\mathcal S_g$ be the small Schottky–Jung locus, defined as the intersection of the Schottky–Jung loci associated with all nonzero characteristics. Donagi's conjecture. The small Schottky–Jung locus is equal to the Jacobian locus:

$$\mathcal S_g=J_g.$$

The Jacobian locus is known to be an irreducible component of $\mathcal S_g$, but equality is not established in the supplied text.