I think the difference is the power brick probably doesn't allow the +5 and +12 to decay at the same rate.  That must affect whatever logic they used to determine that they had a loss of power while operating.  Remember, it has to also handle the situation where the device has been turned off normally, then unplugged and plugged back in.  In that case, I suspect they don't want the NAS to power up automatically.  I know I've done stuff like this with avionics, but I actually had hardware assist designed in to make the job easy.  I'm not sure how they did this in the DNS-321, or what hardware support they had available to determine that they were operating when power was lost.  Since they can't really spin up the disks to decide whether to power up, I suspect they write an "operating" flag to the FLASH when they're running and clear it when they're powered down normally, but that's just a SWAG.