And why exactly is it so impossible for matter to become an indistinguishable state? Why can't entropy go down in such extreme conditions? Sure, all our experiments in relatively low gravity seemed to conserve "information", but what gives us the right to extrapolate that to black holes?
It's not like the second law of thermodynamics is really a law anyway. It just says that normally, entropy is so unlikely to decrease spontaneously that, for all intents and purposes, we may safely assume it never does. As long as the system is big enough, because violations of this "law" are already causing trouble in nanotechnology. If only a few atoms are involved, nothing keeps the entropy of the system from decreasing every now and then. But for large enough collections of atoms, sure, they are very unlikely to suddenly organise themselves, temperature difference are very unlikely to evolve the "wrong" way, etcetera. In the kind of conditions we have been able to observe so far.
But black holes... I can readily imagine them destroying information, in fact it seems extremely likely to me that they do, from an intuitive point of view. So why are scientists having such a big problem with that? Sure, entropy always increases in sufficiently large "normal" systems but black holes are anything but normal. I really don't see any compelling reason for them to conserve entropy.