The police have had access to the video of them getting wanded through the metal detectors since day 1, I refuse to believe they would have taken this long to notice 'oh hey they still have their watches and wallets'. While it's not impossible that he made the story up, he's also gone a lot of trouble to support the lie, like calling home to talk to mom, hiring extra security or whatever the article said, which makes that whole theory very complicated.
Rio being a crime infested third world shithole is a much simpler explanation, and until I see very solid evidence to make me think otherwise, that's the theory I'm going to stick with.