How come these are marked as public domain if YouTube identifies them as copyrighted material if used in a video?
These are in fact in Public Domain (or, as the law may require, CC(0) as Public Domain isn't valid in some countries). The reason YouTube flags these is because their copyright infringement identification system - dubbed "Content ID" - checks the audio for specific parameters (peaks, tempo, dynamic etc.) that cannot be fooled by compression (which changes the entire binary presentation of the file). These matches are imperfect - they often manage to match specific music (often correctly!), but copyright holders often hold copyright on more than just the music. This can include performance, arrangement and so on. Taking all of that together - the matches are sort of accurate (the music matches), but still INVALID (different performer, different arrangement etc.). Please file disputes against these matches each time you receive one. Please check often to see if you've received any such ContentID matches. When filing a dispute, either claim that you have a license (if your country doesn't respect Public Domain and you must otherwise use CC(0)), or that the music in itself has been released to the Public Domain. Always provide a link back to the page you downloaded the music from.