"their music" can be publicly presented

Unfortunately for you, any music that's not your creation and that is
used in your video is considered "copyright infringement". The huge
music/media corporations like UMG, Warner and Viacom don't just
"own their music", they also "own the rights" to them -- that means
how and where "their music" can be publicly presented.

Thus, they're apparently 100% within their rights to claim the music
in your video as their own -- especially if you have not paid them for
"licensing fees", "distribution rights", "royalties", and/or "expressed
written permission" to use and "broadcast" their music on YouTube.

If you did use their music, that is considered part of the often-heard
warning: "Unauthorized duplication, reproduction, retransmission or
redistribution -- whether in whole or in part -- without the expressed
written consent of [insert company name here] is strictly prohibited.
All rights reserved. © " Their concern isn't just you but other people
who could conceivably download, copy or listen to their music "free"
and "on-demand" without ever having bought it, nevermind that your
video might be tarnishing the artist's image.