I haven’t read the article fully, but I believe the specific tax havens weren’t at fault. Rather, it was intermediary companies used to form these offshore accounts. I’m sure the intermediaries assured their clients that privacy would be maintained, and only limited information would be passed on to the Corporate Registrars in each tax haven. A number of tax havens make available a limited search capability of their corporate registries, so not too much information was divulged there. Apparently, the weak link were companies involved in setting up LLC’s, etc. for clients. For the Panama Papers, it was an actual Law Office.