I have to say, the policy is definitely overzealous, despite the policy being quite obviously stated. OP should take some of the balme for not reading/paying attention to the information presented. I've booked SQ online many times and based on my experience they do warn you on quite a few places during and after you book the flight.
One way to avoid the check is to use a Visa or Master Card with the extra online verification (Verified by Visa/Master Card). This is how I book tix for my fiance on my card when she needs to travel.
That said, I like CX's policy that someone mentioned earlier if it is indeed that way. To charge full fare is just ridiculous.
OP can contest the charge with AmEx, but doubt they would win it unless they can get SQ to make an exception which would clearly be common sense in this case.