How do I permanently disable the scrollbar? I set the Show Scroll Bars setting to "Automatically based on Mouse or Trackpad", but it constantly appears.

I do not want the scroll bar to automatically appear, or appear when scrolling. I want it to never appear. OS X provides the "Always" option, but I'm looking for a "Never" option. 

How do I permanently disable the scrollbar?
I found this application that claims to do what you asked for.

The LionScrollbars