For what it's worth, TiddlyWiki can save itself on the filesystem even with Firefox (user gets prompted to allow access). I don't know how it works though and when I tried it seemed to be quite buggy.
According to Wikipedia they use FileI/O, a Mozilla API for accessing the filesystem, which from what I can tell it's more directed at Addons than webpages.
If you're calling requestFileSystem() for the first time, new storage is created for your app. It's important to remember that this file system is sandboxed, meaning one web app cannot access another app's files. This also means you cannot read/write files to an arbitrary folder on the user's hard drive (for example My Pictures, My Documents, etc.).