From the Wild Style trivia on IMDB:

Recent DVD/Video release replaces original tracks that Grandmaster Flash is cutting up in his kitchen (“God Made Me Funky” and “Take Me To The Mardi Gras”) with generic Chris Stein-produced soundtrack music. This was because the original artists whose records Flash was using wanted $8,000 each for the rights to include the tracks in the re-release.

(YouTube link is not the original version.)