>> Why would system tables like to scan an index that is not being used by the user?
Kindly confirm whether a DB Reindex or Reorganize scripts are running in the background..
Because that would be done by your system to keep the index statistics up to date without an INSERT or UPDATE or DELETE statements..
Even If you have Auto Update Statistics Set to ON, this might occur..
Because Auto Update Statistics will be performed by Server in times when ther is less load on the server.