The old answer was that the cutoff occurs at infinity, that is, at the end of the external universe.
It seems that you treat "infinity" as a particular moment in time. However, "the end of the universe at infinity" simply means: it will never happen. There will never be an end to the universe in such ase, therefore nobody will be able to see it, regardless if they are falling into the black hole endlessly or not (and if they live forever or not).
So, going back to your original question "Can matter really fall through an event horizon?", if it takes finite time than the answer is a decided "yes", otherwise the answer is "no". The end of the universe (presuming it happens "at infinity") has nothing to do with it.