I believe Wesabe had an implementation that did this.

From http://blog.precipice.org/why-wesabe-lost-to-mint/

   Wesabe built our own data acquisition system, first
   using downloadable client programs (partially because
   that was easier and partially to preserve users’
   privacy)

Technically, they could provide a self-hosted version. But that may not be a very profitable business. Also, screen scraping needs continuous updating as the bank's interface changes.