While I am unable to narrow down where the error is occurring I have got a fix that can be applied on set.
When you load your prop in the Set Workshop, click on the User Image area and if there isn't an image on it already select Change Image. Load a new still image (jpeg, png or dds) and then press on the Up arrow to reposition the texture. You should see the screen area turn black and the top of the image become visible at the bottom. This is because the mapping coordinates have become offset by -1 on the Y axis, you need to move the image back up to fill the area correctly using the up arrow.
Go in to Directors view, load a video and it should work exactly as you'd want it to now.
The reason that still images look ok and videos do not is that stills auto tile (so you are actually seeing a copy of the image directly above the one you load) and videos do not, so you get the top line of pixels stretching to fill the space.
Mystery solved! We'll keep looking at this for a bit to see if we can automate the solution, but for now, happy image moving