Had a situation over Swan Island over the Carribean one day in the clouds at FL350. We reported Swan Island on the hour at 350. One minute later World reported Swan Island at 01 at 350. I asked them to confirm their position report and they confirmed it. I then asked them what direction they were going and they were on a 130 heading. We were on a 180 heading so knew we were clear. A few minutes later the controller cleared them to FL370. No reports were filed but things like that happen a lot down south. TCAS is a wonderful thing down there.