Just guessing but...

Since the URL "https://myupdatedconfigfile.com" indicates SSL, you should check with the web master to see if the server requires your web client to send credentials (some do - and that is really what the exception is indicating). If it is the case that the server requires credentials, you need to find out if it requires a client cert (likely if you VPN using a CAC card) or something else.

Once you have the particulars of what the server requires to allow you to establish a connection, you'll need to google how to present that type of credentials using the WebClient.