Whoa, hold your horses! Tell your parents that although there will be no issues with Customs in bringing back that bottle (it might be two since there are two of them), there will be issues with Japan security at Narita and TSA in DTW if they try to hand carry! Japan will politely but firmly confiscate at the checkpoint at NRT where all transiting passengers are screened.

What I would do is this instead. When your parents arrive in SIN, tell them to buy the scotch in duty free - the shops are after passport control but before the baggage carousels. Then have them take the liquor past Singapore Customs and straight to the hotel (they can bring in one litre each of wine, beer and hard stuff each, ie total 3 litres of liquid per person, albeit max one litre of each type). Then what they should do is bubble wrap the liquor in the hotel and pack it into the suitcase to check in on the return trip, problem solved. As long as the bottle is packed tightly in the suitcase so that it doesn't move around when the case is bumped, it won't break. If it's a bottle that's in a box, I'd stuff the box with clothing or newspapers so it doesn't shift around inside.

BTW the prices in SIN duty free for liquor is quite good, they won't regret buying it there. If they want to buy cigarettes, they can do this when they leave Singapore (ciggie prices amazingly cheap), that can be hand carried and will not be confiscated.