I'm not sure if Basecamp still allows the use of your own SFTP server for file storage, but they did very early on. I used Joyent's Strongspace as the file backend and it worked flawlessly. It would be great if this functionality was brought to Project Pier.
You should find it relatively easy to write a new storage backend, I would suggest using the file system one as a good example. One of the key benefits of using ProjectPier though is the ability to host it yourself, so using outside storage is less necessary. I think there is also a patch floating around that provides a storage backend using Amazon's S3 storage.
I tried to search for both the file system example that you mentioned and the S3 patch to no avail. You wouldn't happen to remember where they are?
Not being lazy, just couldn't find them. :)
In the release package, the code that allows you to use the file system vs the db as a storage backend is the code that I was referring to as an example. Next time I come across the S3 code, I'll repost here.