[T-A]

> There is a huge mistake in this reasoning!

No there isn't. As far as external observers are concerned, an object falling into a black hole takes an infinite amount of time to cross the event horizon. It vanishes from sight because its emissions get red-shifted beyond detection range, but in principle you could still see it however far in the future you care to go, "frozen" in place over the horizon, still approaching it asymptotically.