SQL should not generally run as local system, it should run under a minimal privileged domain account.
You got the error because SQL did not have permission on the folder with the backup. Instead of switching to local system, just go to the folder, change the security and grant the SQL Server service account full control.
Gail Shaw
Microsoft Certified Master: SQL Server, MVP, M.Sc (Comp Sci)
SQL In The Wild: Discussions on DB performance with occasional diversions into recoverability