The problem - see http://kb2.adobe.com/cps/155/tn_15586.html
A Flash movie embedded in an HTML page does not receive tabbing focus/key events when the page first loads in a web browser. In addition, in browsers other than Internet Explorer, it is impossible to pass the focus to the Flash player object without first clicking on the player. This is completely inaccessible to those who require mouse alternatives and for whom clicking is impossible.
In order for a Flash movie to capture key events, the movie itself must first be given focus from the browser. Web browsers do not automatically give keyboard focus to Flash movies, or any other embedded content.
Try it below: just hit the tab key to move through the buttons (shift+tab to reverse order) and hit ENTER or SPACE to simulate a mouse click on any element.