This has started to bother me. From numerous sources, I read/hear that to an outside observer, we would never see our brave/stupid/suicidal astronaut friend cross the event horizon of a black hole because of time dilation. This seems incorrect to me.

As a mythical starship approaches the speed of light, we see it going faster. Time dilation only affects the difference in our frame of reference relative to that of the crazy-ass pilot who keeps opening his throttle wider. Gravitational time dilation appears to be identical to time dilation due to acceleration, so we would not see the astronaut who is falling into a black hole fall ever more slowly, we would see him (or her) accelerate toward the speed of light, which is the speed at which they would seem to cross the event horizon.

Why would we, the amateur public, be given this misinformation? Is there a communication problem that even astrophysicists like Tyson cannot cope with? Or am I completely wrong?

And how do we figure on a singularity? Beyond the event horizon, we have no way to know what the internal dynamics would look like. Is it possible that a very massive object could simply have an event horizon without forming a singularity?

Or even have a gradient so extreme that we could not realistically discern that it is a full event horizon? Something only a little larger that its Schwarzschild Radius would look, for all intents and purposes, like a black hole.

From what I read, Sagittarius A*, by its mass and volume estimates, has an average density of about 2 atmospheres of Earth air, so it could easily contain an object that is simply very large, rather than a singularity. The math that we use for black holes suggests a singularity, but is that math valid beyond the event horizon?

To me, it seems likely that if matter cannot reach or exceed the speed of light, the notion that it could bend spacetime infinitely with its mass is equally implausible. We observe what appear to be black holes, but can we be sure that we are seeing genuine event horizons? If a mass can bend spacetime infinitesimally close to having an event horizon, with some kind of Zeno’s Paradox preventing, shall we say, full closure, would it matter from our point of view (being not inclined to dive in to find out)?