What the authors take as their notion of a Schottky group is what usually gets called a classical Schottky group. In the H3 / S2 case, there are open sets in Schottky space disjoint from the locus of classical Schottky groups...Thus, even in the simplest case their techniques necessarily break down...
Maybe the issue disappears in higher dimension or in the complex case. I don't know. But this must be addressed before the main theorems of the paper can be accepted."