I can confirm that the mp4 I downloaded is not (detectably by my desktop video player) corrupt. I am not sure what it is, but it is not corrupt. (Except for the filename, but that is because javascript is brain-damaged as regards strings.)
I also have cookies and javascript disabled. Maybe the javascript is messing with the video.
It's just a gray screen for me in both HTML5 and Flash players, though if I download the video and play it in MPC-HC it's fine. Weird stuff!