Not many Americans have such a tradition. Sounds like movie hype to me. I have not heard of Japanese with such a tradition.
Actually, it's a pretty well known tradition. Not just for wedding rings but family heirlooms in general, Grandmas pearls, Moms wedding dress. I think it might have something to do with that wedding rhyme: Something old, something new, something borrowed, something blue.

I think that how it goes

The movie is called Blood Diamond with Leonardo Di Caprio and Djimon Honsou. I have not watched it myself but will, to see what judgement I come up about the issue after watching the film.
It's a good movie, a real eye opener in the sheer amount of blood, death and corruption that happens just so a girl can wear a shiny rock on her finger.

It's sad that people know this but turn a blind eye...nobody wants to know that their precious wedding ring is a Blood Diamond and probably cost someone their life...or their families lives.