I suppose it's a philosophical matter, but it seems legitimate to me to view this as matter moving out of the event horizon, even if the mechanism of that motion is very indirect. One's answer would depend on whether you consider a photon that travels to your eyes from the sun after reflecting from a mirror to be the same photon that was originally emitted by the sun, because it carries that photon's energy and information, even if it was actually absorbed and then coherently re-emitted by the mirror after a staggeringly complicated sea of particle-particle interactions.

Okay in terms of philosophy sure you could maybe make an argument, I don't know.

What we can, however, say that is more tangible is that the make-up of Hawking radiation cannot depend whatsoever on the matter that falls into the black hole apart from three properties: mass, charge and momentum. Other than those three properties, all other information that crosses the event horizon is lost and can't escape.

So, if one black hole was formed purely from 1 kg of protons with 0 momentum, and another black hole was formed from 1 kg of positrons with 0 momentum, these two black holes would be indistinguishable from each other. There would be nothing that could be emitted by either black hole via Hawking radiation or any other mechanism that could allow you to deduce that one was formed from protons and the other from positrons.

It's in this stricter information theoretic sense that nothing escapes from beyond the event horizon of a black hole.

That's a very contestable point; there are strong reasons to believe the information content is indeed preserved (albeit in a scrambled form).

https://en.m.wikipedia.org/wiki/Black_hole_information_parad...

Energy, even if it doesn’t convey information is still a “thing”. Photons with a black body spectrum - thermal noise, are still things.

Hawking himself originally had an idea of photons that tunnelled through the event horizon as a possible mechanism.