I am a physicist but I think he is more or less technically correct. We have photos of black hole like objects but no evidence that they conform to the object described in general relativity except in broad terms. There are the obvious issues with quantization, for example, but there are also multiple ways we can formulate GR-style theories which give different black-hole solutions which have not yet been disambiguated by experiment.
I don't think there is any harm really in calling the objects we have "taken photographs of" (these images are model dependent, so to call them photographs is a bit of a stretch) "black holes," but if we want to be totally precise a black hole is a specific concept in GR, a theory which most people think is incomplete, and we have only found some correspondences between that theoretical object and some observations in the world.
It is an interesting exercise to apply this sort of thinking to (for example) electrons. Do we know electrons exist? In an informal sense, obviously, but in a more detailed sense I would argue care must be taken. We know that QED, for example, is not renormalizable, and thus we ought to be careful to distinguish the notion of "QED electrons" from "Standard Model Electrons" from "the things that leave exposures on our detectors."
But we do know considerably more about the qualities of the physical objects we measure and call electrons than we know about the qualities of the physical objects we measure and call black holes. I don't think its unreasonable to be careful about these things.
Observation of collapsars nicely corresponds to GR predictions about collapsars without event horizon, there's no real need to invoke black holes here. You might call them black holes, but I imagine people will be confused why these kinda black holes don't have event horizon, singularity, coordinate discontinuity, information paradox, cosmic censorship and all that stuff black holes are famous for. They already conclude there's evidence for event horizon, because it's a widely advertized feature of black holes and there's a photo of black hole.
Yes, we have photos of collapsed stars, some of which were above the Tolman–Oppenheimer–Volkoff limit and became black holes. When they are not above it, they either become white dwarf or neutron stars.
Volkoff's calculation demonstrates that a star above the limit begins to collapse. It doesn't support the claim that they already became black holes, especially this can't happen globally with galilean synchronism even under slightly unrealistic assumptions. In the end, it's a mathematical calculation under assumptions; if you want to connect it to reality, you need to understand what it claims exactly and estimate what error is introduced by difference between its assumptions and reality.
A photo of a star is cool, why not give a prize for it. Or maybe they use attention economy. You can't exactly blame them for attention economy, can you?
Photos as the only evidence of existence are a very convenient way of claming the nonexistence of something that reflects zero light. The baby-out-with-the-bathwater is that it also means there's no proof for anything outside the visible range of light, that's too small to show up on a CCD, or that predates the camera. Or you.
On the other hand, arbitrary conjecture in absence of evidence should be treated exactly as such.
It's worth noting that there are a number of phenomena for which we have built detectors to find this mysterious "dark matter", all of which have failed to turn anything up whatsoever. In fact they are less than useless in that we still don't know if any of the proposed mechanisms can even be ruled out yet. The experiments achieved basically zero information gain in that regard.
Occam's razor flashes bright in the cold dark of space.
