If YouTube is hosting content which infringes copyright it may not yet have been flagged for removal. This in no way absolves Facebook from addressing copyright issues when such shared content appears on their site.
Here is Facebook's policy on copyright...
http://www.facebook.com/legal/copyright.php
"If you're not certain that you are legally authorized to use the content, do not upload it to Facebook. If you have done so already, you should remove it. If you don't own the copyright to content you wish to post, posting it without permission of the copyright holder might be a violation of the law."
"Facebook video is meant for uploading and sharing personal content. We've designed the application to discourage misuse, and our users agree to upload only video of a personal nature that is about them or their friends, or created by them or their friends."
"If you repeatedly infringe other people's intellectual property rights, we will disable your account when appropriate."