Coulton himself does not own the rights to Mix-A-Lot’s lyrics, of course, but,
according to the U.S. Copyright Office, “the copyright of a derivative work covers ... the additions, changes, or other new material appearing for the first time in the work."
Even if Fox got permission for the
Glee cover of “Baby Got Back” from Harry Fox (which they undoubtedly did), they are also required to seek permission from Coulton for use of his “additions”—chords, phrasings, rhythms, and so on—that make his arrangement unique (and choir-boy friendly).