Hello, what version are you on?
I found this for version 9x: An administrator that has access to the system settings, management interface and database information. Typically, an administrator can also manage departments, groups, and users. Note: For new installations, the administrator must also have the agent role enabled. For those upgrading from a previous version, the administrator will not have the agent role enabled and can only access the reports and settings areas of the management interface. Administrators must have the Agent role and be part of groups in order to view global tickets and live chats.
Try giving them the Agent Role and they may be able to search tickets globally?