Youtube polices the site by complaint. If someone claims copyright infringement, hateful or harmful speech or actions, indecent actions (usually sexual content) then the site monitors take the action they believe appropriate.

If they get a complaint from any logged on user saying that John Smith (for example) is singing a well known Bob Dylan copyright song - or is singing my song, then they will probably just take the film down, no questions asked. If the content is too racy, too hateful or too ugly and they've gotten a complaint - they will just take it down.

I suspect it is also possible if the videos get too few "views" they will take them down too.