Place the video clip on two tracks -- I'm using a .jpg image here.
Give the lower track a 'White Box' effect and adjust it so only your plain white becomes transparent.
Adjust the 'Brightness' setting of the upper track to darken everything.
If all goes well you will see the unaltered mages of the lower track against the background color you have given to the upper track. Most obvious potential problem is having any 'plain' white present other then in the background.
Note: these thumbnails had a slight shadowing against the original white background which shows as a light outline agains the black.