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Why do some users see more Reports than their Role allows them to?
When you set up a Role, you can limit the reports that are available to users on that role. If however, you have "activated" or given access to the role "Everyone on the Internet," your users will see the "superset" of all reports available to their Role as well as the Everyone on the Internet role.
You will need to limit the reports available to the Role assigned to Everyone on the Internet, or turn it off altogether.