Dijoin-clutter tau equals two conjecture

Let $(D=(V,A),w)$ be a weighted digraph, and let $\mathcal{C}(D,w)$ be its clutter of minimal dijoins. Suppose that $\mathcal{C}(D,w)$ is minimally non-packing.

Dijoin-clutter $\tau=2$ conjecture. The weighted digraph $(D,w)$ has a dicut of weight two.

This is presented as the weighted-dijoin specialisation of the $\tau=2$ conjecture for clutters. The supplied text does not state a resolution.