Trivia: In the fight at the petrol station they are using guns instead of swords (which were used in Shakespearian times), however, when it's said "draw your swords", the dialogue didn't have to be changed for this part, because the film directors made it so that the make of the gun was "sword". Also, when Capulet says "Hand me my Longsword", he reaches for a rifle, most likely from the same factory that made the Sword pistols.
Trivia: The song that the Montagues sing throughout the movie, 'A Pretty Piece of Flesh I Am,' is a quote from the play.
Trivia: The wings on Juliet's masque costume are re-used in another Baz Luhrmann film: One of the Diamond Dogs in Moulin Rouge has the wings on her costume.
Trivia: In Romeo's first scene (between him and Benvolio) there is a billboard in the background for "The Merchant of Venice Beach." A reference to Shakespeare's Merchant of Venice.
Trivia: Pete Postlethwaite (as Friar Laurence) is the only actor who speaks his lines in iambic pentameter, the rhythm of speech Shakespeare's plays are written in.
Answer: Whatever songs are in the movie were licensed for distribution by the film production company for a fixed price. It is impossible for there to be later fees somehow incurred on the production company just because the group is more popular. However, it's conceivable that Radiohead only allowed their song for use in cinemas but not television.