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Or...
You can set the publish settings options under the HTML tab for "Window Mode" to "transparent windowless". Any transparent parts of your animation should let the HTML background show through, but it will really slow down the animation.
Putting the relevant piece of the background into the animation means the animation has to be located in exactly the right place on all browsers (and can never be moved) and color depth/image compression have to be exactly the same on the orphan piece and the original background.