Option to send notification off but system still sends

Option to send notification off but system still sends

Hi we have disabled the option to send notifications to requesters when a ticket is closed. However the system still sends a notification anyway. This is very disruptive, for example we try to close a ticket, the system sends a notification to the user, but this user's inbox is full so we get a message from the System admin saying that the user's inbox is full. As a result the ticket is reopened. This happens anytime we try to close these types of ticket. And we would like requesters to have the ability to reopen thier tickets.
 
Regards