Ashenbrenner et al. state the Hyperbolisation theorem as follows
Let $N$ be a compact, orientable, irreducible $3$-manifold with empty or toroidal boundary. If $N$ is atoroidal and $π_1(N)$ is infinite, then $N$ is hyperbolic.
But in the following remark they say that (1) any closed atoroidal 3-manifold with infinite fundamental group is hyperbolic, as a consequence of Leeb et al. Theorem H
Any smooth action by a finite group on a closed hyperbolic 3–manifold is smoothly conjugate to an isometric action.
This should be a remark about how the hyperbolisation theorem also holds for non-orientable manifolds, but I'm puzzeld at how the irreducibility condition is dropped. I don't understand this theorem implies (1). Can anybody explain me?