That isn't what "peer to peer" means, though. Peer to peer means that peers (the aforementioned browser, smartphone and tablet) communicate directly with each other.
Also, how does CouchDB keep things secure if clients can sync apparently any data? I'm assuming there's something there, but nobody else has explained this.
First, CouchDB supports security and validation.
Second, for CouchDB replication is just another client connecting to a DB; it's handled the same way anything else is.
As a result, we have the notion of filtered replication. The server-side CouchDB won't tell anyone secrets they don't need to know - be they clients or client-side DBs. At at the other end, the client-side CouchDB has some validation to stop "bad" data going into the database by accident, and then the server-side CouchDB has the same validation again. People can compromise their client DB all they want, but eventually it all ends up on the wire as plain old HTTP requests interacting with a plain old REST API.
In many ways - as far as security goes - the client DB is a red herring. The server ONLY speaks a well-defined REST API, and has validation and security to deal with malformed or malicious API requests. The fact that those requests are generated by a client-side DB based on data entered into it via JS commands is neither here nor there; a Backbone app would generate the exact same requests based on more-or-less the same JS commands. If you can secure any REST API, you can secure CouchDB.