The weak closure property for matroids over hyperfields

Let $F$ be a hyperfield and let $\mathcal{M}$ be an $F$-matroid with vector set $\mathcal{V}^*(\mathcal{M})$. The Weak Closure Property is the assertion that, for all $X,Y\in \mathcal{V}^*(\mathcal{M})$, one has

$$(X\boxplus Y)\cap \mathcal{V}^*(\mathcal{M})\neq \emptyset.$$

Weak Closure Property. The Weak Closure Property holds for all matroids over hyperfields. This would characterize a broad class of tract-like coefficient systems for which vector sets retain a weak form of additive closure; the supplied text does not indicate whether the assertion is proved or remains open.