Under the ATX design and similar psu's, they provide a low-level system wake-up. In other words, its always warm and able to quickly power-up from kybd.(some key), remote activation(modem) or network setup. In some kybds. if no "power LED" then you have a leaky ckt. that activates(led) showing some power present, though weak. Better kybds. with no power LED, usually are unlit. Alot depends on your system make-up, etc., you can check the bios setup and see under pheriphals or similar what if any "wake-up" setting is set for. If you open your system case, you may find a small LED always lit, a visible reminder not to pull cables, etc. unless power is OFF, plus it usually is showing power is good(open to debate) but some mtrbd. makers call it that. Anyways, you can always pull the AC plug to truly shutdown system after proper shutdown.
tada -----Willy