Video playback doesn’t involve the same privacy concerns as recording, so there’s no obvious reason for Firefox to treat them the same way.
I don’t notice a problem in a simple video tag where the source video is in the same directory (locally accessed on file://):
<video controls="controls" preload="none" width="560" height="320">
<source src="big_buck_bunny.mp4" type="video/mp4">
</video>
That’s static HTML, not scripted, if that makes a difference.