The stronger Terao conjecture for minimal degrees of line arrangements

Let ${\mathcal A}$ and ${\mathcal B}$ be arrangements of $d$ lines with isomorphic intersection lattices

$$L({\mathcal A})\cong L({\mathcal B}).$$

Let $r({\mathcal A})$ denote the minimal degree of a Jacobian relation. Stronger Terao conjecture. If

$$r({\mathcal A})<d/2,$$

then

$$r({\mathcal A})=r({\mathcal B}).$$

This stronger form is motivated by the failure of lattice invariance of $r$ in general, but the source also reports counterexamples for arrangements with the same weak combinatorics, so its status is not resolved by the supplied excerpt.