Just seeing this this work. I just cut and paste the <video> markup from http://www.nutshell-videos.ed.ac.uk/barbara-webb-insect-robots/ into the “text” editor (rather than “Visual”) of WordPress.
I had to adjust the width to get it to fit in my odd, fixed width theme.
Alternatively from the visual editor I can do “Add Media” and select “Insert from URL” and then paste in the URL to the video, in this case http://podcast.is.ed.ac.uk:8080/Podcasts/cseresearch/webm/inf-barbara-webb.webm, and then I get the following:
