Fässler–Orponen restricted Marstrand conjecture for space curves

Let $I\subset\mathbb{R}$ be a compact interval, and let $\gamma:I\to S^2$ be a $C^2$ curve satisfying the escaping great circle condition

$$\operatorname{span}\\{\gamma(\theta),\dot\gamma(\theta),\ddot\gamma(\theta)\\}=\mathbb{R}^3$$

for every $\theta\in I$. Let $Z\subset\mathbb{R}^3$ be analytic. Fässler–Orponen's conjecture. For almost every $\theta\in I$,

$$\mathrm{dim}\,(\gamma(\theta)\cdot Z)=\min(\mathrm{dim}\, Z,1).$$

This is a restricted Marstrand-type projection statement for directions lying on a space curve that does not remain in any great circle to second order. The paper's abstract says that this conjecture is resolved, but the supplied excerpt does not state whether the result proves or disproves it.