When you try one of these scenarios:
TF401009: The TFS service account NT AUTHORITY\LOCAL SERVICE cannot access network shares. Change to an account that can access the backup path. TF400997: SQL Server service is running as NT AUTHORITY\NETWORKSERVICE. Please change this account to an account that can be granted permission on the backup path.
Scheduled Backups end up with failure, even if you've granted permissions to the NT AUTHORITY\LOCAL SERVICE and the NT AUTHORITY\NETWORKSERVICE accounts on the backup path.
There are two methods responsible for verifying account permissions to access the backup path:
which use the account types defined like this
LocalSystem 0x01 LocalService 0x02 NetworkService 0x04 User 0x08 Computer 0x10
Instead of verifying account permissions they check account type, and return an error if the JobAgent service log on as:
LocalService NetworkService Computer
and the Sql Server service log on as:
LocalSystem LocalService NetworkService Computer
So, to run Scheduled Backups without errors you have to change the JobAgent and the Sql Server service accounts to User account. After you create scheduled backup or restore the databases, you can go back to the default accounts.