When I click the checkbox "Permissions to settings" and then click 'save changes', this particular setting is not being saved, so my client will be able to see other website data if they so wish by changing the plugin settings.
Are you getting an error or anything? I just tried it on the 3 WordPress blogs I have access to, and all 3 saved the setting as expected. What version of WordPress are you using? The ones I tried it on were running 4.4.1.