I haven’t studied his paper in detail, but maybe I can provide come context as to the ongoing debate it is part of.
The larger frame is that of the black hole information paradox—roughly, the fact that information is generally conserved in all quantum processes, due to the way quantum systems evolve (‘unitarily’, meaning roughly that all probabilities must sum to one, and implying reversibility, i.e. it can be run backwards, and thus, any information from earlier times can be recovered by just running the evolution backwards) in the absence of measurements, while it seems to be lost when it comes to black holes. Basically, black holes evaporate via Hawking radiation, and what they evaporate into can be viewed as a thermalized gas, i.e. a state that contains no information due to the fact that all the particles are distributed randomly. But this seems to imply that the information of anything thrown into it is lost. However, we also expect that this evaporation will ultimately have a description in terms of a quantum theory, where unitarity, and hence information, ought to be preserved.
Indeed, at least for certain black holes in a special context, such a description is known, thanks to something called the AdS/CFT-correspondence, where a gravitational theory in a higher dimensional space can be described in terms of a quantum theory on its boundary. Unitarity indeed holds in this context, so many people believe it should also hold in more realistic settings (Hawking himself famously retracted his earlier stance, that information is, in fact, lost, thus conceding a bet with John Preskill).
However, a recent argument due to Almheiri, Polchinski, Marolf and Sully (AMPS) poses some difficulties for that resolution. Basically, in order to transport information out of the black hole, after roughly half the evaporation time, the black hole must be maximally entangled with the Hawking radiation it has already emitted (entanglement being a type of quantum correlation that exceeds classically possible correlations). However, due to a generic feature of quantum field theory, the radiation modes just inside the black hole horizon and just outside of it must similarly be maximally entangled. But, entanglement is monogamous: if system A is maximally entangled with system B, it can’t be entangled at all with another system C.
This in itself isn’t necessarily a problem, due to something called ‘black hole complementarity’, a proposal by Leonard Susskind that, roughly, says that there are two different stories that one can tell about a black hole, that of an infalling observer, and that of one staying outside. The insider now can verify the entanglement between modes across the horizon, while the outsider can verify that of the early Hawking radiation with the black hole (by waiting for more radiation to leak out). But nobody, it was thought, can do both, and so, each tells a consistent story; this proposal entails that the interior of the black hole and the far-away Hawking radiation are, in a sense, two ‘complementary’ ways of looking at the same stuff.
But AMPS now showed that there actually is a way to measure both entanglements in this setting, and thus, that it apparently violates monogamy of entanglement. To resolve this, they proposed that in fact, there is no black hole interior, and that thus there is no entanglement across the horizon; but this means, again due to a generic feature of the vacuum in quantum field theory, that the state of the degrees of freedom at the horizon must be thermal—anybody falling into a black hole will be incinerated by a massive blast of radiation!
This, however, is in conflict with the principle of equivalence in general relativity, which entails that, for a sufficiently large black hole, there is ‘nothing special’ at the horizon, because locally, every spacetime can be made to look flat. This is basically the foundational principle of general relativity.
So no matter what we do, it seems that something’s gotta give—either black hole evaporation isn’t unitary after all, and information is lost, or the equivalence principle breaks down, or for some reason the local field theory description of the black hole horizon is wrong. (For a good summary of the argument, see this blog post by John Preskill; he also has a couple more discussing the issue in more detail.) None of these options are especially appealing to physicists, and so the broad feeling is that the AMPS argument is wrong; but nobody can, so far, put their finger on why. This has led to a great amount of debate, with entire workshops devoted entirely to the discussion of this issue (narrowly avoided the ‘hotly debated’-pun there).
Hawking now appears to propose that the problem is avoided, because no actual event horizon ever forms; as I’ve said, I haven’t read the details of his proposal, so I can’t really comment on it. It is, however, only one in a long line of proposals, and time will tell which one, if any, can be made to work in detail, and I personally don’t think Hawking’s has a priori a greater chance than any of the others.