If you only want to post the link and you want anchor text to the titke of the video then use this instead: <a href="http://http://www.youtube.com/watch?v=FrHkKXFRbCI">The Story of Keep Calm and Carry On </a>
and the result will look like this in the post or page The Story of Keep Calm and Carry On
When uploading a VIDEO to YouTube there are copyright issues. But as for the responsibility after that, it lies with the person who uploaded the video. If you just put the video in your blog, you’re taking in good faith that the uploader had the rights. Sometimes they don’t and the video gets deleted, but your blog is not at risk.