  In [5], a rigidity result was obtained for outermost marginally outer trapped
surfaces (MOTSs) that do not admit metrics of positive scalar curvature. This
allowed one to treat the "borderline case" in the author's work with R. Schoen
concerning the topology of higher dimensional black holes [8]. The proof of
this rigidity result involved bending the initial data manifold in the vicinity
of the MOTS within the ambient spacetime. In this note we show how to
circumvent this step, and thereby obtain a pure initial data version of this
rigidity result and its consequence concerning the topology of black holes.
