Consider the classical solution of a black hole and imagine some matter crossing the event horizontal so that it cannot escape the black hole. I don't remember in the case of a rotating black hole, but in the simpler solution of a non rotating one, a distant observer should see this matter appear to slow down and freeze near the event horizon, never quite reaching it..I can't remember if the same is essentially true in a real back hole, i. e. one that rotates. If it were, and the physical picture were really that simple , then it would probably mean that from an external perspective, not a single piece of matter has ever actually entered a black hole in all the time the universe has existed. Under intuitive causation you might therefore not expect to actually observe Hawking Radiation, as to the external observer nothing will have reached the event horizon in all this time. Evidently this picture is wrong somehow.
So my question is: what is wrong with this simple picture that I have presented and why would we expect to see hawking radiation?