Ok I took a look at the demo for SWFAddress. It is using anchor names (the same idea that allows you to link to a specific location within a page). For example:
http://asual.com/swfaddress/samples/flash/#/contact/

Note the # character. So that would allow you to change the displayed URL without actually leaving the page since the browser thinks you are linking to a named anchor within the page. Kind of a neat trick.