Tested this with both 7-2.7 and 7-2.x-dev.
When you store a video file, original or converted, using the private file system the video file will not play back on iPhone, iPod, and iPad. Switching it back to public files and then re-uploading the video so it stores in the correct location the video will play back just fine.
It appears to work just fine on other devices.
Also, not sure if this is related: http://drupal.org/node/1293310