You are right that copyright is an issue with video upload sites. Youtube and other similar sites that allow users to upload videos are protected by the princilpe that service providers are not responsible for the content that their users publish. They are however required to act promptly to take-down notices.
ISPs that offer web space and web hosting providers are all protected by this principle.
I don't think that sites that have anonymous uploads aer afforded the same protection. That is to say, if youtube didn't have user accounts they could be liable for the actions of the uploaders.
Mike