The stress-linked pair component conjecture

Let $G$ be a graph and let $u,v\in V(G)$. An $\mathcal{R}_d$-component $G_0$ of $G$ is a component with respect to the $\mathcal{R}_d$-matroid structure used in the paper. A pair $\{u,v\}$ is $d$-stress-linked in a graph when it satisfies the stress-linkage condition defined in the paper.

Stress-linked pair component conjecture. If $\{u,v\}$ is $d$-stress-linked in $G$, then there is some $\mathcal{R}_d$-component $G_0$ of $G$ such that $\{u,v\}$ is $d$-stress-linked in $G_0$.

The source states that an affirmative answer would imply another conjecture in the paper. The claim is attributed there to Conjecture 6.4 of the cited work.