The concept of public domain resources is not a difficult one, you don't need special legal training or advanced math to understand the idea that copyright expires and that works whose copyright has expired are free to all. There is no mechanism to even assert public domain status on Youtube.
You have to wait and offer it as a defense if subjected to a copyright infringement claim, and the copyright infringement claim is presumed to be valid and the claimant is the first judge of the public domain assertion.
Youtube didn't invent the system, but they are far from being helpless victims as you imply.
