This is a case of a writer being terrified by his publishers' lawyers - not by the law. His publishers' lawyers say he can't quote the lyrics and both he and his publisher believe them. Lawyers always err on the side of caution. I strongly doubt that the music company would take the publisher to court for publicizing the song by using the lyrics as chapter headings - after all, publicity can only lead to more sales, to the benefit of all rightsholders - the lyricist usually, and/or the music publisher.
Techdirt has not posted any stories submitted by Chris Zielinski.