[video], gray "Download File" box

Using the [video] short code to stack mp4, ogg, webm videos.

On the desktop, it all works well. However, on mobile devices (tested two Androids and an iPad mini) neither the video nor a still frame appear. Instead there is a gray box with the words “Download File” under a link.

Since I’m getting the behavior on both iOS and Android, I have a hunch there is something amiss on the server side, but I cannot figure out what.

ALREADY TRIED:

Videos: Cut with both file converters and running their through Adobe Premier. No change.

Plug-ins: Disabled all plug-ins. No change.

Raw: Tried a raw (no WP template) page. No change.