Simon, I appreciate you expressing your own experiences with these issues. You are right it is easy for hate speech to creep up even if that is not the intention of the site or the moderator. When emotions get heated common sense doesn't always stay with the person and they will say inappropriate stuff and responses can lead to even more inappropriate talk. Unless you have a moderator who that is their full-time job it is not possible to keep up with all of the moderation that a popular site or group needs to keep it compliant with the site's code of conduct.
When information is taken down due to a copyright infringement that is a legitimate issue that anyone can bring up. Copyright law is extremely complicated and even the idea of fair use is not as simple as some people think it is. Putting up a fair use banner in the front of a YouTube video doesn't negate some people's breaking of the law.