> I may well be wrong

Unfortunately, you are. The information that is lost is what went into the black hole in the first place.

It's not strictly a quantum problem: if black holes have no hair, then we cannot tell by looking at a spherically symmetric non-rotating black hole if it was formed by one spherical shell of infalling matter of mass M, or two concentric spherical shells of infalling matter of mass M/2, or three of M/3, etc. When we add electromagnetism to the picture, we get Hawking radiation inversely proportional to the black hole mass; but that mass does not encode the number of shells or their composition, just their total mass.

When we add in quantum electrodynamics, we find that Hawking radiation has a thermal spectrum (so, cold photons for a stellar-mass black hole, but when the black hole is very small you'll get electrons and positrons too; and potentially the whole zoo of particles if we use the full standard-model as the quantum field theory). But we could start with a black hole formed by squashing together neutral composites (positronium, atoms) and with some probability get out nothing but photons: no massive particles at all. With some smaller probability we get mostly photons but also electrons and positrons. The main problem is that we are stuck talking probabilistically about the spectrum Hawking quanta even if we know every single detail of what we threw into the black hole; there is no unitary evolution from known-in-every-detail state to known-in-every-detail state. The "every detail" part is the information that is lost.

There are a variety of ways one can try to deal with the conversion of "we know every detail" (a pure state, quantum mechanically) to "we can only talk probabilistically" (a mixed state, quantum mechanically), and some are listed in the wikipedia page you link to. Hawking's final paper is yet another approach, and throws away the idea that black holes have no hair; that is, a black hole cannot be described with a small number of parameters (dominated by mass and angular momentum) but rather develop an enormous number of parameters encoded as perturbations of the vacuum. Those perturbations in turn influence the spectrum of the Hawking quanta in such a way that it is fully predictable -- even though it looks like a thermal bath, the vacuum perturbations ("soft hairs") fully determine it. It an idea is worth further investigation, but is not much more compelling than several alternatives.

One problem is that when we take an exact analytical black hole solution to the Einstein Field Equations of general relativity, we have "no hair" as a mathematical theorem. If we perturb around such a solution we generate observables that closely match what we see of candidate astrophysical black holes in the sky. Hawking wants to treat astrophysical black holes as even more different than the theoretical models, and while that's not a crazy idea, it's also not very parsimonious as many many many more perturbations ("hairs") are necessary than the minimum required to match the observed systems, and it's not clear that a "no hair" black hole must be measurably different from a "soft hair" black hole.

(More detail here https://news.ycombinator.com/item?id=18327614 )