In discussions of Black hole information paradox, people usually argue that the falling observer shall not see radiation at the horizon or near the horizon due to the equivalence principle. That is, for a falling observer, what around him is just vacuum in a locally Minkowski spacetime. This is because, for a falling observer, the Christoffel connection vanishes. The problem is, if the equivalence principle holds, the asymptotic static observer at infinity also has the same status of a "free-falling" observer. Because, spacetime is asymptotically flat and the static observer is a free-moving observer in locally Minkowski spacetime. Then why shall the static observer at infinity observe Hawing radiation?
Consider a static observer far away from the black hole (but not at infinity) and the usual free falling observer crossing the horizon. The latter follows a geodesic, while the former must accelerate to not fall in.
In analogy to the Unruh effect, the accelerated observer will see particles. All of this can be made less naive by computing the Bogoliubov transformations relating the regular vacuum at the horizon with the singular one in schwarzschild coordinates.
Now, since the observer far away from the hole will see a flux of radiation, the one at infinity will see it too.