I find that video very confusing. Some of it is just plain wrong (the singularity in a black hole isn't an infinitely dense point, for example). Some of it has to have been taken out of context if it's not wrong (the stuff about Planck units being the smallest units of space and time isn't true in relativity; maybe it has meaning in some quantum theory of gravity - I don't know). So by the time I get to your timestamp, I've been saying "no", "not really", "maybe", or "that's an enormous over-simplification" about every ten seconds for nearly six minutes. Just to set the scene.
The bit you are talking about isn't talking about GR, anyway. The video doesn't seem to be clear about whether it means that a universe exists inside a black hole, or if the not-quite-singularity eventually forms another universe, or if this kind of causal language doesn't really describe this kind of thing (both the first two wordings pop up - the third is my own suspiscion). It does say "speculative" at least twice.
So my answer is that I don't know any more having watched this video than I did before. It doesn't provide references and doesn't provide a consistent model that one can consider. The claim is still flat wrong in general relativity. We don't know which, if any, of the successor theories that we have is correct, so it would go under "not impossible" for now.
I believe that Lee Smolin proposed something of the sort of thing they are talking about. I don't know any more than that, but following up on work Smolin did might be a start.