Interval graphs are boundary-distance-matrix reconstructible

Let $G$ be an interval graph. A graph is called BDM-constructible if it is uniquely determined by its boundary distance matrix (with the relevant order and boundary fixed). Interval-graph BDM conjecture. Every interval graph is a BDM graph. This claim establishes another positive graph family for the broader boundary-distance reconstruction question; the supplied text does not state whether the claim has been proved beyond the assertion shown here.