My Ubuntu box auto-updated a bunch of packages with names like "libavcodec" and "ffmpega". Hey those got mentioned on all those troubleshooting pages with which I totally failed to use Pitivi edit a simple video this weekend. So I tried again... and Pitivi was still pretty broken. But then I tried kdenlive (a different video editing program) again, and that worked!!1! Now you can see what that video was supposed to look like. See, those pixels were supposed to be a bunny.
Thanks for the update, mysterious Linux video library maintainers!