Best guess is that the iPhone is firing up a seperate application (Quicktime?) to play the video and it doesn't share credentials with Safari. Since it needs credentials to access the file and doesn't have them it fails.
Most desktop browsers open the media file in the same application via a plug-in.
Not 100% sure this is right (don't own an iPhone) and I'm not quite sure what could be done to fix it. Do you have web server logs from when an iPhone has failed to open the movie file?
Dave Dietz