Yep, looks like it should work.
The result is a video box with no video.
I checked the video link by entering the media into post. Video works as a typical tag opening outside of the post vs. video playing in post (inline).
Yes, I agree the path shouldn’t make a difference, just thought I’d throw that out as an idea.
I’m selecting video by navigating to the Media library.
What’s interesting is that this code/page with the [video mp4] tag seemed to work just last week. The only thing I recall is upgrading to WP 3.2.1.