Ziegler's nonfreeness conjecture for generic cuts of free arrangements

Let ${\mathcal{A}}'$ be an essential and free arrangement in ${\mathbb{K}}^\ell$ with $\ell\geq4$, let $X$ be a generic subspace with $\dim X>2$, and let ${\mathcal{A}}'\cap X$ be the restriction defined by

$${\mathcal{A}}'\cap X=\{H\cap X\mid H\in{\mathcal{A}}'\setminus{\mathcal{A}}'_X\}.$$

Ziegler's nonfreeness conjecture. For ${\mathcal{A}}'$ and $X$ as in Ziegler's generic restriction conjecture, the arrangement ${\mathcal{A}}'\cap X$ is never free; equivalently, a generic cut of a free arrangement is not free. The source presents this as an implication Ziegler said would follow if the preceding conjecture were true; no resolution is given.