And, Terry, I couldn't agree more: to say "'The First Time' by Roberta Flack" does convey the idea that Roberta Flack wrote the song, not just that she had the biggest hit record with it.   
In that connection, let me also point out that I've heard some "covers" singers criticized roundly for "not writing their own songs" -- with those criticisms coming from people who seem to believe that "singer/songwriters" such as Sheryl Crow or Garth Brooks or Ian Tyson are the composers/lyricists for all or most of their "greatest hits." That's often not the case.