Converse gluing conjecture for Alexandrov spaces

Let $X,Y\in \text{Alex}^n(\kappa)$ be Alexandrov spaces with non-empty boundary, and let $f:\partial X\to\partial Y$ be a homeomorphism. If the gluing $X\cup_fY$ is an Alexandrov space in $\text{Alex}^n(\kappa)$, then the converse gluing conjecture. $f$ is an isometry. This conjecture is presented as a converse to the gluing theorem in Alexandrov geometry and is stated as a consequence of the relatively maximum volume rigidity conjecture; its resolution is not given in the source.