Right - but Hawking said that as matter goes into a black hole it is destroyed.
Thus, he was wrong.
Starting in the mid-1970s, Stephen Hawking and Jacob Bekenstein put forward theoretical arguments based on general relativity and quantum field theory that not only appeared to be inconsistent with information conservation but which did not account for the information loss and which stated no reason for it. Specifically, Hawking's From calculations[4] indicated that black hole evaporation via Hawking radiation does not preserve information. Today, many physicists believe that the holographic principle (specifically the AdS/CFT duality) demonstrates that Hawking's conclusion was incorrect, and that information is in fact preserved.[5] In 2004 Hawking himself conceded a bet he had made, agreeing that black hole evaporation does in fact preserve information.
However, the article is talking about Hawking radiation, which is a different aspect of the black hole issue. From Hawking radiation
Hawking radiation is black-body radiation that is predicted to be released by black holes, due to quantum effects near the event horizon. It is named after the physicist Stephen Hawking, who provided a theoretical argument for its existence in 1974.[1]Hawking radiation reduces the mass and energy of black holes and is therefore also known as black hole evaporation. Because of this, black holes that do not gain mass through other means are expected to shrink and ultimately vanish. Micro black holes are predicted to be larger emitters of radiation than larger black holes and should shrink and dissipate faster.[2]
I hope that helps.
I think part of the problem is that the Daily Mail screwed up the meaning of the paradox.