In their 2008 paper "Torelli theorem for curves over finite fields" Bogomolov, Korotiaev and Tschinkel mention in the beginning of Section 9 that absolute Galois groups of curves over $\mathbb{F}_p^{alg}$ are free profinite on countably many generators. However, they do not give reference, and after talking to some colleagues I am at a loss with regard to the status of this statement.

How does one derive this fact (if it is true)?