Personally, I don't think you should always pick an image from the video. It actually depends on the situation.
I've got an example from my recent UX review: a product site with a short video, demonstrating product features, etc.
This video was surrounded with a text, describing the main product idea. And the start image for this video was a random image from the video itself, but, as we all know, picture worth a thousand words, so I suggested to get an refined image describing the main product idea and place it as video start image.
Now we have a text, an illustration for that text and a demo video combined together.
Another example is about an image from the movie itself. There is a local online tv-series streaming service which I use every day. It has a lot of titles, which are grouped by seasons and for every season there is a single page with all episodes. And every episode has a start image taken from the episode itself. It's okey, until start image is a spoiler image, i.e. something I don't really expect to see before I watch the epicode by myself!
From the other hand, at YouTube I wish to have a video starting image taking from the video itself so I can decide whatever it's a right video to watch (there are a lot of music videos with a different video track, etc).
So, it actually depends on the situation.