First, I admit to having asked a Spanish law professor and judge to explain what this (IMHO) poorly drafted text means. As Jonay mentions, the law actually reads "recabar" rather than "ejercer. la tutela." What "recabar la tutela" means in this context is that if the "Responsable" (person in charge of the "archivo" or "registro" or whatever) denies access to certain information to someone who has applied for access to that data, the applicant must be informed that he has the right to petition the Data Protection Agency or other equivalent agencies (i.e., the data protection agencies in the autonomous communities) to overturn that decision and grant access to the requested information.