General-position peel restriction conjecture

Let $d$ be a metric of strict negative type on a finite space in general position, let $\mathcal{I}$ be a subset of $\operatorname{peel}(d)$, and let $d|_{\mathcal{I}}$ denote the restriction of $d$ to $\mathcal{I}$. General-position peel restriction conjecture. If $d$ is strict negative type on a finite space in general position and $\mathcal{I} \subseteq \operatorname{peel}(d)$, then

$$\operatorname{peel}(d|_{\mathcal{I}})=\mathcal{I}.$$

This is the second weaker conjecture proposed in response to the exotic and brittle counterexample; the source gives no proof or resolution.