The compatibility-degree exchangeability conjecture

Let $\mathcal{A}(B)$ be a cluster algebra, let $x,x'$ be cluster variables, and let $(x\parallel x')$ denote their compatibility degree. Compatibility-degree exchangeability conjecture. If

$$(x\parallel x')=(x'\parallel x)=1,$$

then there exists a set $X$ of cluster variables such that $X\cup\{x\}$ and $X\cup\{x'\}$ are both clusters. The theorem preceding this statement proves the converse implication: variables occurring in clusters that differ by exchanging $x$ and $x'$ have compatibility degree one in both directions. The conjectured converse would characterize exchangeable pairs through the compatibility degree, but the supplied text gives no resolution beyond saying that it is open.