SQL 2008 R2 - Does SS2K8 control what is logged into the Error Log?

Good Day to All,

Mutliple SS2K8 Ent X64 environments.  I force a Restore Failure and find the event logged in Error Log.  When I do the same thing on another SQL Server (same config).  The failure is not logged.

Message
BackupDiskFile::OpenMedia: Backup device 'E:\SQLdata02\Backups\ssde\PROD01\SQLSERVER_DATABASE_ADMIN.bak' failed to open. Operating system error 2(The system cannot find the file specified.).

Does SS2K8  control what is logged into the Error Log?

Thank You - Covi