Speed is the only factor that will give you a drag required message. And it is based on the speed entered in the FMS descent page or 3/3 as you said.
So, why the discrepancy between the Boeing manual (DRAG REQUIRED message at VMO-16/349 knots) and the statement in the Big Boeing Book that being more than 15 knots above FMC target descent speed will set off a DRAG REQUIRED? Which one is right? If FMC target descent speed was 280 and it took 300 to stay on path, would I get the message?