Lyric discussion by ProfessorKnowItAll 

Cover art for Rio lyrics by Duran Duran

I always figured it was about kidnapping a supermodel/pornstar. The first two verses are him obsessing in a John Hinckley-loves-Jodie Foster way, believing that him seeing her everywhere ("I've seen you on the beach and I've seen you on TV") is a sign and her sex-kitten attitude is meant just for him, and in the "at the end of the drive, the lawmen arrive, you make me feel alive...I'll take my chance, cuz luck is on my side or something..." is the thrill he's feeling after abducting this model/pornstar and running from the cops.

Otherwise, how do the verses about police arriving fit in with a love for a woman or America?

Hate to say it but I think your right, that is the only explanation I can think of that matches all of the lyrics.

Hate to say it but I think your right, that is the only explanation I can think of that matches all of the lyrics.

Not only that but the last verse it would make sense it was talking about people looking for her from the north to the south, but my brain has a resistance to thinking that because then it would be a truly horrible song but then again it also fits.