When trying to add a backup manually through All Backups | Add Backup, a pop message titled "Some entries from the backup file were not added" occurs with the details the above error from the title is seen, and no backup file is added, although the required administrative permissions were set across the farm and the SQL server.
Also an error as the following is seen in the Console log:
01/01/2010 09:35:18 2788:1 [Error] RM4SP.CBackupFileInfoBase+SqlAccountNoAccessToAdminShareException: Account "NT AUTHORITY\NETWORK SERVICE" needs to be granted with local administrator permissions on the computer "ComputerName" or the file \\ComputerName\Drive$\Backup.BAK does not exist. ---> System.Data.SqlClient.SqlException: Cannot open backup device '\\ComputerName\Drive$\Backup.BAK'. Operating system error 5(failed to retrieve text for this error. Reason: 15105).
RESTORE HEADERONLY is terminating abnormally.
This can occur mostly in a singleserver SharePoint installation, as the error indicates that the SQL server is running under a network account rather a domain account, hence issues with the network account not having enough permissions.
If this is a singleserver installation, or if the SQL is running under a network account, then adding the SQL server computer account (the account from AD which ends with $ sign) to the local administrator group on the console machine (the machine \\ComputerName seen in the error message) should resolve the issue.