Circuit-cocircuit intersection conjecture for q-matroids

Let $M$ be a $q$-matroid with circuits $\mathcal{C}$ and cocircuits $\mathcal{C}^*$. Suppose

$$\dim(C\cap C^*)\neq 1$$

for all $C\in\mathcal{C}$ and $C^*\in\mathcal{C}^*$. Then Definition gives a relation on the $q$-matroid $M$.

Circuit-cocircuit intersection conjecture. Under these hypotheses, Definition is an equivalence relation.

This is presented as a sufficient condition suggested by the paper's examples, but the supplied text gives no evidence that it has been proved or disproved.