Earlier quoted context omitted.
A traveler can reach it all right, but only from his own point of view. From the point of view of almost everyone else in the Universe, including us on Earth, it will never ever reach it. It's like the traveler has jumped into an other universe "located" in an infinitely distant future.
So let's say I fall into a black hole. And then four billion years later, someone else falls into a black hole from the same direction. From an outside perspective at a point nearly infinitely far away in time, we would seem to slow until we are right next to each other at the event horizon, correct? Does this mean everything that falls into a black hole crosses the event horizon (from their perspective) at the same…
Incorrect. You would still be relativisticly separated and this would be measurable especially at infinity. You would be accelerated by 4 billion more years and would have that much more relativistic acceleration in signals you sent out. This could be monitored and the outside observers would be able to tell the difference. The second person would be more blue shifted compared to you (clock ticking faster).
> Does this mean everything that falls into a black hole crosses the event horizon (from their perspective) at the same moment, a moment which only exists from the crossers' perspective, as it is always infinitely far away from a perspective outside the event horizon?
No, their clocks tick away just like they always did. They cross the event horizon just as they thought they would. They do 'see' the universe's clocks accelerate along though. But they do cross it nonetheless.
Note: By 'see' I mean that the rest of the universe blue shifts to infinity and the Lorentz transformation causes the incoming radiation to be directed to directly in front of you. Only when you cross the event horizon, the incoming radiation from the 'outside' turns into an infinitely energetic (infinite blue shift) beam of radiation coming directly at you. In your reference frame, you vaporize.
This is my BHs are soooo crazy. When we run the numbers, the Quantum Mechanical effects really do affect things. Infinitely small wavelength light isn't something we can really handle, the Plank Length should come into play. But General Relativity don't care. This is why we really need Quantum Gravity, because nothing makes sense.