If you run this command in an ASP.Net web application, it runs under the context of the Identity of the application under the Application Pool. Change the application pool to run under a privileged account which has permissions to the UNC Share folder.
If you let the application pool run under the Network Service account, then provide the read/write permissions to the UNC share folder for the network service account.
Also note that the SQL Server service can run under a different set of account - local/network. This account needs to let SQL Server create backups on the UNC. This is valid in the case, you are not creating backups from ASP.Net web application.
This should resolve the issue.
Hope this helps.