Boundary-kernel characterization of modifications of Stein spaces

Let $\Omega$ be a domain in a complex manifold, let $\Sigma_\Omega$ denote its plurisubharmonic kernel, and let $\mathrm{b}\Sigma_\Omega$ denote the corresponding boundary kernel. A modification of a Stein space is a complex space obtained from a Stein space by a proper modification.

Modification characterization conjecture.

$$\Omega\text{ is a modification of a Stein space}\quad\Longleftrightarrow\quad \mathrm{b}\Sigma_\Omega=\emptyset.$$

The preceding result proves one direction under the relevant hypotheses, while the source's remark notes that emptiness of the boundary kernel is not necessary for the particular sufficient criterion previously discussed. The stated equivalence is presented as a conjecture, and no resolution is given.