Can't edit event reminder without Administer CiviCRM privileges

Although creating a reminder for an event simply requires the Access CiviEvent permission, editing a reminder requires Administer CiviCRM. A non-admin can't see the main Schedule Reminders page (though that seems reasonable), but they can see the Schedule Reminders tab on the event. When they attempt to edit a reminder, however, they get Access Denied. The form is the sam e