The girls were fans of Martin Scorsese movies, think The Godfather (1972), and the song was originally supposed to be "Al Pacino's Waiting", but that didn't have the required rhythm. It didn't scan well. But Robert De Niro's name, that had the necessary flow.
There exists the notion that the song was written to console a young girl who got raped and was off the idea of any future relationships, except maybe with an idol. This was accredited to Siobhan Fahey. She has since shirked this off as nonsense. It might have been dreamed up by the media or exaggerated upon by fans. But there are darker undertones in the music video, e.g. being followed by a stranger, fitting in with this. It is most likely true.