Source: Wrestling Observer newsletter
The reason why a lot of the WCW theme music is now being used on the WWE Network and not dubbed in with generic music is because WWE has settled some deals and because of a settlement with Jimmy Papa. Papa produced music for WCW and World Class Championship Wrestling. Papa sued WWE in 2012 claiming that WWE had used his WCW theme music and Badstreet USA. He wrote Badstreet USA for Michael Hayes.
Papa sued Hayes, WWE, and Jim Johnston for copyright violation because the claim by him was that WWE said that Johnston wrote the songs. The case has been settled and WWE can now use the music.