For one observer X happens. For a different observer X cannot happen.
Nothing can ever reach the black hole, yet if you are that thing, you reach the black hole.
That's just a disagreement between observers about the measurement of time, which we already know experimentally is a real effect when two observers accelerate differently. The atomic clocks on GPS satellites run detectably more slowly than atomic clocks on the ground, for this reason; and they do so as predicted by relativity.
An observer on a spaceship that is accelerating sees his atomic clock telling him that he reaches a given location in space at T+
x seconds, while the observers on the ground see this happening later, at T+
y seconds - we can demonstrate this to be true, and it conforms with the theoretical prediction. When the observer and the spacecraft move together,
x =
y, and
y -
x = 0; as the spacecraft accelerates,
y increases, and so
y -
x also increases - the difference between when the pilot of the spacecraft thinks the mission reaches a given location, and when the observer in mission control thinks this has occurred increases.
If one of a pair of twins joins the space program and gets to go on a trip to a distant star at a sizable fraction of
c, then when he gets home, he will find that his brother is far older than him - that
y -
x >> 0. That's not a paradox; it's a straightforward consequence of relativity, and is confirmed by experiment.
In the case of a spacecraft falling into a black hole, the vessel crosses the event horizon at T+
x seconds as observed by the doomed pilot; and at T+
y seconds as observed by mission control back on Earth - and in this case, because for a black hole, V
e =
c, the theory tells us that in this case,
y = ∞; and so
y -
x = ∞; so mission control won't see the spacecraft cross the event horizon until the year ∞. There's no paradox here; it's simple mathematics. For any point arbitrarily close to the event horizon,
y -
x is an arbitrarily large number, so at any given point in time, the spacecraft can be observed by mission control as being closer to the event horizon than it was at any earlier time (although the brightness with which it can be imaged may well rapidly fall below any possible ability to detect it).