AFAIU this is pretty much what they are saying. The gravitational field of the black hole is not as simple as we thought it would be (i.e. it cannot be fully de

AFAIU this is pretty much what they are saying. The gravitational field of the black hole is not as simple as we thought it would be (i.e. it cannot be fully described by just a few numbers like mass, angular momentum and charge) and it carries information about the original matter that formed the BH. This information then manages to "escape" along with the Hawking radition as the gravitational field influences the emission of said radiation.