Without linking to the "controversy" ... more specifically, can a Jewish artist take a tune from a secular source and make a Jewish variant of it -- and then make a profit, by selling CDs with the tune or performing it in concert.
I am not a lawyer, and will not address this from a legal angle. Nor am I giving a pesak halacha here.
However, classically, this is what has been done over and over, even for some secular songs. The tune to the Star Spangled Banner is a rip-off of a Russian drinking song. Many chassidish niggunim are Russian or Polish drinking songs or marches. Case in point -- the Tetris niggun.
Further, where the audience is small and specific - a niche market - then this is a classic case of zeh nehneh vezeh lo chaser - "this one benefits and this one does not lose" - which is halachically permissible. People who buy Uncle Moishe are typically not the same ones that buy Raffi, and people who buy MBD are typically not the type to listen to German rock bands. So I would say "no." Schlock Rock to regular rock - well, they are targeting the same audience as a kiruv endeavor, but still, one would have to see if people really would buy one as an alternative to the other (I would tend to doubt it, but don't know).
Meanwhile, copying a CD or tape where you really otherwise would have purchased it -- this can certainly be cast as zeh nehneh vezeh chaser, which is more problematic.