So after you got the note, what happened? Did they delete the video? Did they shut down your channel? I am betting that what they did is put an advertisement on the video page.

This is how they are responding to the issue of all the covers, etc. you speak of. Rather than shutting it all down, they let you keep it posted, but the party with the copyright claim gets ad revenue. I can see how that would be unacceptable for many -- in which case you have two options: 1) Prove that you have the right, i.e. fight them; 2) Take the video down.

Otherwise you accept it.