Perhaps this is different on osTicket as I used many tickets and when a ticket is closed the name of the technician either is moved to "Closed by:" or the ticket is kept under "Staff:"
The reason why is because if the tech decides to go to the closed tickets closed by the specific tech, the tickets will be displayed under the name of the given tech.
Contrary to osTicket one most find the ticket under closed ticket by performing a search under the company name and/or ticket number is know and/or a know string to be placed in the search box.
If I perform a review of the tickets the "Staff:" has no name and since there is not "Closed By:" title the ticket is to be assumed to be close by the last person touching the ticket. But it could also be possible that each of them closed the ticket. So the condition still seems to be not met or at least it seems like that.