Yes videos on YouTube are in Flash.
Videos on the YouTube application for iPhone are converted to a format that can be played back by QuickTime AFAIK, maybe m4v.
So he didn't use a browser, go to youtube, and clicked on a vid?
He used some 3rd party app?
No, there is a standalone app that is standard on iPhone and comes packaged with it.
Actually, Flash Player can playback MPEG 4 videos (mp4, m4v...) with the H264 codec since version 9.0.115
QuickTime Player in the iPhone YouTube app and Flash Player on youtube.com might play the exact same files...