Historically, it has always been cheaper to travel from the US to SIN than to NRT on AA. Not sure why, but the fare differences can be quite dramatic. Recently, JFK-SIN on AA in J (JFK-NRT-SIN r/t) was about $5400 but just go JFK-NRT (using the same AA167/168 flights) and it was over $2000 more on the same dates.
Fares are market based and not always mileage based.