Are Black Holes Neutrino Factories? That is.. are they an intense source of neutrinos? If so, then the center of almost every galaxy would be a neutrino factory.
Your question must be referring to this announcement, and the qualification is for highe energy neutrinos, not generally neutrino factories.
The team of researchers is still trying to develop a case for how Sagittarius A* might produce neutrinos. One idea is that it could happen when particles around the black hole are accelerated by a shock wave, like a sonic boom, that produces charged particles that decay to neutrinos.
This latest result may also contribute to the understanding of another major puzzle in astrophysics: the source of high-energy cosmic rays. Since the charged particles that make up cosmic rays are deflected by magnetic fields in our Galaxy, scientists have been unable to pinpoint their origin. The charged particles accelerated by a shock wave near Sgr A* may be a significant source of very energetic cosmic rays
The paper is here.
We investigate whether a subset of high-energy events observed by IceCube may be due to neutrinos from Sagittarius A*. We check both spatial and temporal coincidences of IceCube events with other transient activities of Sagittarius A*. Among the seven IceCube shower events nearest to the galactic center, we have found that event 25 has a time very close to (around three hours after) the brightest X-ray flare of Sagittarius A* observed by the Chandra X-ray Observatory with a p-value of 0.9%. Furthermore, two of the seven events occurred within one day of each other (there is a 1.6% probability that this would occur for a random distribution in time). Thus, the determination that some IceCube events occur at similar times as X-ray flares and others occur in a burst could be the smoking gun that Sagittarius A* is a point source of very high energy neutrinos. We point out that if IceCube galactic center neutrino events originate from charged pion decays, then TeV gamma rays should come from neutral pion decays at a similar rate. We show that the CTA, HAWC, H.E.S.S. and VERITAS experiments should be sensitive enough to test this.
So it is still a hypothesis, which needs patience as high energy neutrino events are not very common and coordinating results from several experiments has its difficulties. It is possible that this is the explanation for high energy neutrino events, and black holes are the source. But not really a factory, as the numbers reaching us are low.
In isolation, black holes probably won't generate reactions powerful enough to produce neutrinos. However, in cases where there is a ring of gas around the black hole (called an accretion disk, and likewise the system is now referred to as an accreting black hole), then they probably will produce neutrinos. Likewise, active galactic nuclei are also strong candidates for neutrino production. My cautionary language is purposeful here, as to date there haven't been any detections of neutrino sources outside of our solar system. Its not that we haven't seen neutrinos from this distance, but rather that we haven't seen enough to zero in on any specific origin, so we are left with largely theoretical calculations.
In regards to dark matter, the discussion begins to get rather involved. Neutrinos are one candidate for something called "hot dark matter". Here, "hot" just means that the particles are moving very quickly. For various reasons, hot dark matter falls a bit short when explaining certain aspects of the early universe. The theory of a mixed hot and cold dark matter was popular up until about the late 1990's, but has since fallen out of favor. Currently, scientists are looking for a combination of cold dark matter and dark energy. I'd recommend checking out the links below for more detailed explanations: