The Adobe Flash player operates in a sandbox. This means it can't access files on the users's machine without explicit permission. You can do this by, as you said, browsing for a file using a FileRef (file reference).
You can, however, access data placed on a server machine (relative to where your swf is stored), or across domains (swf on one server, data on the other). To access data across domains, you need a crossdomain.xml file placed on the server containing data that tells Flash what it can and cannot access.