To a distant observer a black hole 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 event horizon and returns to latency, or redshifts in frequency, as the particle climbs back out of the gravity well. Neutrinos carry kinetic energy and nothing, or next to nothing else. The kinetic energy carried by the neutrino converts to rest mass of the daughter particles if the neutrino interacts with a nucleus. The weak nuclear force should not be able to discriminate between the original kinetic energy and the blueshift portion of a neutrino's total kinetic energy near the event horizon.
Kinetic energy is kinetic energy, period.
Therefore gravitational potential energy converts to kinetic energy as a neutrino approaches the event horizon and then converts to rest mass if the neutrino interacts with a nucleus. Rest mass is observable in all reference frames and does contribute to the increase in mass of the black hole upon particle capture. This is very simple. Just two particles and two different energy outcomes depending only on whether the two meet near the event horizon or not. There is more to this of course.