If you want to transfer restricted data to the Internet, the solution is not necessarily to give them access to the restricted network segment via the Internet. In fact, I would strongly discourage it as you describe it. What you ask is actually quite complicated to implement in a responsible manner.
For illustration, you have two network segments. A DMZ and a private network. Databases live in the private and Web servers live in the DMZ. For security purposes, you fully restrict access to and from the private network using a firewall. If the DMZ is compromised and the authentication data is stored on the server, the cracker will be able to access the restricted data.
This is where encryption requirements and key management techniques come in to place, which are exampled within the PCI DSS. If you do not have an advanced encryption architecture, you will still risk the data in case of compromise even if it is not stored in the DMZ.
You could potentially implement a ETL and batch out the data. Often, this solution dictates a need to have the data encrypted using strong encryption and then transferring via your preferred protocol. Once the data is encrypted, the methods used to transfer it can be substantially more flexible.
Your exact situation is going to dictate how much effort is made to establish a production worthy solution. If you a dealing with a one-off request, you might be best off manually satisfying it via a tool such as GnuPG. Otherwise, you might need to build, find or buy an application. An approach that is becoming more common is using a Web application to satisfy the security requirements, while still allowing the data to be accessible to those with less technical knowledge.
