From what I understand, and I haven't really been following it that closely, black holes have still only been theoretical until somewhat recently. Einstein's work hinted at the possibility, and Hawking gets a lot of credit for further developing the concept. The existence of black holes has been widely accepted by the general public, because they have been told so by "science guys", and their understanding of the science is limited.
Even in the scientific world their existence has been taken for granted, but it has been understood among those who specialize in studying black holes, that the evidence was still incomplete. Without having read the articles about this image, I would assume that the image, more or less, proves beyond a doubt that they do exist. But, to even be able to argue the point you would probably need an advanced degree in astrophysics, or a level of understanding equivalent to such. The rest of us simply "have" to accept what we are told.