How do I make a database backup and have it stored locally?

So here's the challenge. I need to use C# to back up a database locally from a remote database server and the only share we have is \\computer\c$.

If the answer is to back up to a location on the remote database server and then copy that local, assume there is not a share on the remote location. Just b/c I have access to the database does not mean I have access to the file system.

This Q/A looks close to what I want, but remember the regular account in the database will not have access to the network. Sample sql script to zip and transfer database backup file

With all of that in mind...anyone done something like this and care to share? Or have an idea of how to do this?

UPDATE: I was being vague on purpose. The context here is this:

1. I do not have access to files on the server where the database is.
2. I am running the C# from the client under the client's credentials, so I have full control of the client computer and can do anything in this domain.

I think I actually have figured out what we are going to do though:

1. Create a special folder in the AppData area of the current user.
2. Create a fileshare to that folder
3. Add rights to Everyone for that particular share and folder.
4. Process the backup based on that share.
5. Remove the share and reset the permissions.

In case anyone is curious what this question refers to: RoundhousE

think I actually have figured out what we are going to do:

1. Create a special folder in the AppData area of the current user.
2. Create a fileshare to that folder
3. Add rights to Everyone for that particular share and folder.
4. Process the backup based on that share.
5. Remove the share and reset the permissions.

In case anyone is curious what this question refers to: RoundhousE