I was looking to do something similar to this. In short, the DOM and all elements are not directly accessible. However, you can hack things up to get at the data. What you have to do is inject your own javascript into the downloaded webpage. Then evaluate the results.
This page shows the mechanism for doing it:
http://iphoneincubator.com/blog/windows-views/how-to-inject-javascript-functions-into-a-uiwebview
Then you just need to know the name of the database and create some javascript to return the values in a JSON string. Use a cocoa JSON parser to create objects from that string that you can use in your native app.