If the problem is that the .swf is visible outside the overflowed visible area, that could be fixed by adding "wmode" transparent as param of the object and as attribute of the embed:

<param name="wmode" value="transparent" />

and

wmode="transparent"

If the problem is that the component start scrolling automatically, there's a "autoscroll" parameter that you should set to false.

I tested it with a vimeo video without overflow problems in FF 3.5, Opera 10.1, Safari & Chrome, IE8 and 7.