if you have another computer, connected to the Internet, you can VPN into it to grab files or just mess around with it. That computer also needs back to my mac turned on (with your apple id tied to it) so you would still have to own the computer.
Then, in airport utility, you can add the feature to your router. Which lets you connect to it, like server, but more like a VPN.
Assuming you have at least two Mac computers running on the same Apple account, you can use Back to My Mac to remotely access one Mac from another. You can read Apple's description of the service and details on how to set up and troubleshoot it HERE.