With CouchDB, a database is at a URL, such as https://my.personal.oauth-protected.domain.com/photos. You can trigger push replication to any other URL, or pull replication from any URL (assuming you are authorized to do so). You can also specify a filter policy to replicate only a subset of the data as needed.
Therefore a web app which respects your freedom allows/encourages you to replicate your data to your own systems, in the same way a developer who respects your freedom allows/encourages you to take the source code and use it as you see fit. For example, you might pull all your data from https://awesome-app.com/your_username and keep it on your laptop's encrypted partition.
Where to replicate to/from, and what the filter policy does is application-specific. The replication plumbing is complete and useful; however, I concede that general-purpose applications are only now being undertaken. The point is, it's encouraging that there is free software which enables "free data" in the cloud-based future of applications.