I got it to work but now they can still edit the other pages too. So it seems like I'm either not able to go that specific with the permissions or I did something wrong.
The permissions it has are:
change_profile, class_map, countries, create, delete_document, edit_document, frames, help, home, list, load, logout, menu_reports, menu_site, menu_support, menu_tools, menu_user, new_document, new_document_in_root, new_static_resource, new_weblink, publish_document, resource_duplicate, resource_quick_create, resource_quick_update, resource_tree, save, save_document, source_view, tree_show_resource_ids, view, view_category, view_document, view_template, view_unpublished