It's possible to do it that way, but it adds some annoying constraints. If you're accessing data locally, it would have to go through a remote server, which causes latency and privacy concerns.
Sorry, I am still not getting this - if the data is local then why not run the app on a server running on the local machine.
Alternately you are trying to access local personal data using a remote app - so you need Google's or HTML5's support for a local database (SQLight I think but in a wrapper).
One instance where it would be nice is if you have your own "browser" written to use XULRunner and want some custom local database for something (say your use of XULRunner is to provide a test harness for automated testing and you want to store the test sequences and value transformations in the database). You have javascript to work with in a sandboxed environment, but isn't hosted on a webpage anywhere. Being able to directly access a database dramatically increases your capabilities and doesn't sound unreasonable. It only sounds unreasonable if you're talking about javascript that gets pushed out to a user's web browser.
NOTE: I wouldn't use this approach, and there's probably better ways, but I can see the potential benefits of it.
