I would be willing to bet:
They are either:
-Paying the publishers to use those songs
-Are not being flagged by the publishers due to a specific relationship they have
-Are changing the content enough to where no rights can be claimed
-Are approved/submitted by the artists for the exposure
Look at all the rap/hip hop mixtapes that get put out on the market. The money in music is not really in selling songs anymore and a lot of these artists give it away for free for other reasons.
No one on youtube is using illegal copyrighted work against the owners wishes after being reported to youtube that I have ever seen and I would not expect that to change.