Fried–Völklein conjecture on projective absolute Galois groups

Let $K\leq\bar{\mathbb Q}$ be Hilbertian, meaning that Hilbert's irreducibility theorem holds in $K$, and let $G_K$ be its absolute Galois group. Assume that $G_K$ is projective among profinite groups. Fried–Völklein conjecture. Then $G_K$ is pro-free. The source presents this as a strengthening of the main theorem discussed for the cyclotomic closure ${{\mathbb Q}}_{\mathrm{cyc}}$, but gives no indication in the supplied text that the conjecture has been resolved.