So you can't just put the <embed /> tag directly into the page?
For the scuba diving cat, clicking on the 'embed' button gives you this:
1<iframe width="420" height="315" src="http://www.youtube.com/embed/bScOj4e0bOQ" frameborder="0" allowfullscreen></iframe>
There's no magic here, you just drop it on your page and it renders.
Or am I not getting what you're trying to accomplish?