The Song:Song Reader is filled out with lots of fragments of songs, and this is one in which only one line/melody was printed.
It appears on the back of "Sorry," in a collection of songs about being sorry: "If You're Sorry, Then Why Don't You Look Sorry?," "Are You Really?," "Stop Being A Baby," and "Don't Apologize." Each one has a different pseudonym attached to it, though Beck wrote the short melody/one line of lyrics for each.
"Don't Apologize" is credited to A. Gadberry, and as far as I can tell the name is entirely made-up (not a reference to anyone or thing).