Why does Safari on the iPhone sometimes display a broken play image for YouTube videos?
You tube sends HTML5/H.264 video to Safari and devices that are unable to reproduce flash video, however, certain videos (those who have ADs and some other features, as far as I can remember)) are still not supported by YouTube in HTML5 format; that explains why you might experience some problems when using Safari and seeing an embedded video. 

In those cases, it’s best to use YouTube’s native application for the iPhone to watch the video.

I have the HTML5 “lab” enabled in youtube and it clearly says that “videos that have Advertising will be reproduced using the Flash player instead”. The video you are showing in your example (this) has advertising in it, hence why mobile safari on the iOS can’t reproduce it. 

In you want to know more about this HTML5 “trial”, you can find all the information on youtube’s HTML page.