Uniform thickness criterion for fibered knots

Let $K\subset S^3$ be a fibered knot, and let $\xi_K$ be the contact structure induced by an open-book decomposition of $K$. Let $\xi_{Std}$ denote the standard contact structure on $S^3$. Uniform thickness criterion. The knot $K$ is uniformly thick if and only if

$$\xi_K\neq\xi_{Std}.$$

This proposed characterization connects uniform thickness with the contact structure supported by a fibered knot. The source explicitly says that the other direction remains an interesting open question, so the equivalence is not established.