A Violation of Energy Conservation
To a distant observer a gravitating body increases in mass only by the energy of particles which fall into it as measured at the defined distant zero position. Gravitational potential energy converts to kinetic energy, or blueshift in frequency, as a particle approaches the gravitating mass and returns to latency, or redshifts in frequency, if the particle climbs back out of the gravity well. This kinetic energy derived from gravitational potential is observable/measurable in only one frame of reference, that of an observer holding a fixed position close to and relative to the gravitating body, and does not contribute to the increase in mass of the gravitating body upon particle accretion.
Consider that a nucleus on the surface of a gravitating mass holds a fixed position relative to that body. Similarly, over a short distance traveled, a nucleus in an accretion disk around a spinning black hole can be considered to be undergoing centrifugal acceleration about equal to and just counter to its free fall geodesic path toward the singularity. For all practical purposes each holds a fixed position nearby and relative to its associated gravitating mass. In either case a freely falling particle, such as a neutrino, will appear to this nucleus observer as gravitationally blueshifted in energy by the factor (1 + gl/c^2),
Neutrinos carry kinetic energy and nothing, or next to nothing else. Much of the kinetic energy carried by a neutrino converts to rest mass of the daughter particles if the neutrino interacts with a nucleus. For example, for Al27, neutrino in, beta negative out, Si27, the proton rich silicon atom is about 5.0 MeV more massive than the Al27 atom - mass derived from the kinetic energy of the neutrino. The weak nuclear force mediating this interaction cannot discriminate between the original kinetic energy and the blueshift portion of the neutrino's total kinetic energy in the frame of reference of the nucleus observer described above. Kinetic energy is kinetic energy, period.
Therefore gravitational potential energy converts to kinetic energy as the freely falling neutrino approaches the gravitating body and then converts to rest mass if the neutrino interacts with a nucleus fixed in position relative to that gravitating body. Rest mass is observable in all reference frames and does contribute to the increase in mass of the gravitating body upon particle accretion.
This is very simple. There are just two particles to consider and two different energy outcomes depending only on whether they interact near the gravitating body or not. One outcome does not violate energy conservation and one does - unless the boundaries of energy conservation are expanded to allow gravitational potential energy, the energy difference between two points in a gravity field, to be made real in all frames of reference through the neutrino/matter interaction mechanism.
There is more to this of course. Neutrino/matter coupling should be much stronger near a black hole's event horizon than elsewhere, a spinning black hole's jets of ejecta are affected in many ways, and there is potentially profound cosmological impact. Reflect and enjoy!
Born, Max, 1962 and 1965, "Einstein's Theory of Relativity," Dover Publications.