Now such a comment shows you have a serious problem - one with not thinking through the problem, and showing a thorough lack of understanding of even the basics of the concept of copyright. Note that every video, every work out there is copyrighted. Also your home videos. The whole notion of those anti-copying groups that say "don't share copyrighted material" is stupid - whether you can share copyrighted material with third parties depends on whether the copyright owner has given permission or not. Simply uploading to YouTube may very well arguably include an implicit permission to share, unless explicitly stated otherwise.
There is a general agreement that linking to material is OK, however this is much more than just linking - this is embedding. Linking is easier: it basically tells "look, over there you can find this or that, you may go have a look". Nothing from the original content is visible in your web site, clearly no copyright infringement.
Embedding a video goes a lot further than that. It is getting quite close to renting a video and showing it to all your friends and all other people that ask. Whether that is legal, generally depends on the copyright license of the rights holder.
If no restrictions on this, you could take all the content of your local newspaper's site, embed it in your web site (using frames or so, so you're not actually copying the news articles to your own web site), and you got your own news web site. I'm pulling it a bit more to an extreme, but it's basically the same: it's embedding. However now you must see the issues this may have.
As I understand it, YouTube has an option to indicate whether you allow your video to be embedded in another web site. If you allow this, there's no issue of course.
A complicating factor in this case will certainly be the fact that the uploader of the video is not the copyright holder of the original material... and that when I see videos from YouTube broadcast as part of a TV show, it very often says (C) YouTube - also something that I have bad feelings about, whether it is true or not.