What OS do you use? Under a Mac OS, I went to this temp folder: /private/var/tmp/folders.501/TemporaryItems/ and I copied the "FlashTmp0" file that was created there and renamed it as a flv (flash video file). I then used Quicktime and Perian plug-in to play flv file. The video from Brightcove is actually h.263 video (not h.264) so you will have to resave it as iPod compatible.
Anyway... maybe someone can help you if you don't have a Mac.