The dual three-color pseudo-disk arrangement conjecture

Let $\mathcal A$ be a pseudo-disk arrangement, and let its members be the objects to be colored. The dual pseudo-disk arrangement conjecture. The members of any pseudo-disk arrangement admit a $3$-coloring such that every point contained in at least $3$ pseudo-disks is contained in two pseudo-disks with different colors. The source calls this the natural dual counterpart of the primal pseudo-disk arrangement conjecture and gives no resolution.