Does the SQLServer account have the rights to write that file? You start off saying you are trying to backup to a remote server, but your example shows writing to a local drive. If you want to backup to a remote server, the SQLServer service must run under a domain account, and have rights to create/write files at the destination (as any network account must).
Also (if memory serves correctly), I had a problem when trying to create a backup of the same backup filename that existed. I named the file with datetime, just like maintenance plan does. Here is a snippet of my vbscript that I used:
' Create a Backup object and set action and source database properties.
sDtStr = CStr(Year(Now))
If Month(Now()) < 10 then sDtStr = sDtStr & "0"
sDtStr = sDtStr & CStr(Month(Now))
If Day(Now()) < 10 then sDtStr = sDtStr & "0"
sDtStr = sDtStr & CStr(Day(Now))
If Hour(Now()) < 10 then sDtStr = sDtStr & "0"
sDtStr = sDtStr & CStr(Hour(Now))
If Minute(Now()) < 10 then sDtStr = sDtStr & "0"
sDtStr = sDtStr & CStr(Minute(Now))
Dim oBackup
Set oBackup = CreateObject("SQLDMO.Backup")
oBackup.Action = SQLDMOBackup_Database
oBackup.Database = sDBName
oBackup.Files = sDBBkpPath & sDBName & "_" & sDtStr & ".bak"
oBackup.MediaName = sDBName & ".bak " & Date & " " & Time
oBackup.BackupSetName = sDBName
oBackup.BackupSetDescription = "Full backup of Yada DB before Updates."
oBackup.SQLBackup oServer
Since you are using a local path during your test, I would suspect that the SQL Service running under local Admin account would work OK (unless that account had its file permissions removed from that directory). However, when you change that path to a remote location, the local Admin will have no possible way to have rights on the remote server, and you will need to run the SQL Service under a domain account to have Windows handle the file permissions.
When you say "specifying a device", I assume you mean writing a backup to a backup device, instead of a file. You do not need to define a device for a remote backup, you can perform a backup using a UNC filename (e.g. //servername/share/backup/mydata.bak). But you will need the SQL Service to be running under a domain account, as Windows will use that account for accessing the remote server (so that the remote server knows which account to check for file permissions).