In the video you're talking about what you store, but I don't quite understand. You store my tweets? All my friends' tweets? Why? Can I export them from your system? Delete them later on? What happens when I close my account?
You can revoke access to the app from here http://twitter.com/account/connections
We don't yet support full delete of all history, but it's on our list.
Also, we are adding support for an api so you can interact with the site/export your history programatically.