I don't know whether Hawking proved an information theory theorem from his mathematical model of the black hole, but the gist of what I got from the layman's explanation is that matter cannot emerge from a black hole, while information can. A grad student trapped inside a black hole might be able to send his report to his doctoral committee via Morse code, although he would never be able to show up in tassel to receive his diploma.
Hawking radiation is matter. And it escapes.