That report is incorrect (it is the Telegraph, after all). Jacintha Saldanha did not reveal any details, but just put the call through to the ward, where the nurse on duty gave out information. The impersonations by the DJs were pathetically poor, perhaps deliberately so, and they never expected even to get through, let alone have someone discuss personal matters, possibly in breach of the DPA (that's not been tested, but it seems very likely).
Worth noting that the call came through to nursing staff because the hospital didn't employ any admin or managerial staff to work out of hours, and the on-call rota was shaky at best, according to reports.
Worth noting also that the Telegraph is a strident advocate of the privatisation of healthcare.