Mmmm.
I can't see the embedded video in the post, or even in the "Topic Review" section at the bottom of the "post reply" page.
All I see is this:
Code:
[YOU TUBE]<object width="425" height="373"><param name="movie" value="http://www.youtube.com/v/BfvGU4W0bvM&rel=1&border=1"></param><param name="wmode" value="transparent"></param><embed src="http://www.youtube.com/v/BfvGU4W0bvM&rel=1&border=1" type="application/x-shockwave-flash" wmode="transparent" width="425" height="373"></embed></object>[/YOU TUBE]
(Without spaces in the bbcode - for some reason vbulletin parses bbcode within "code" tags.

)
However, when I then preview that reply, I can then see the original post with the embedded video working properly at the bottom under "Topic Review". In fact, when I previewed the post, I saw the video embedded inside the "code" box (hence why I added spaces to [YOUTUBE]).
There seems to be some inconsistencies between the "Preview" parsing and what actually happens when a post is made.