ASUS motherboard problems

Don't forget that on any ATX PSU, there is no full "power off" excluding flipping its rocker switch (assuming it has one) in the back. On many motherboards, especially on server motherboards or custom case chassis, you will have diagnostic LEDs that will be lit as long as the PSU is plugged in. 3.3V and 5V do not always completely shut down for a reason - they stop supplying power across device only, but still supply to the motherboard, which the LEDs draw power from.

You can confirm this is true by taking a variable color switching LED (green/red), and plugging it into the power LED header... if it lights up when the computer is off, and reversing it causes it to turn RED.

However, having ALL leds lit up is definately not a good sign at all, definetely a defective PSU or mobo.

Yes, we know that 5v ('PS_ON') will remain on the mainboard after shutdown. In this case, as you quite rightly say, there should not be the additional power to the device LEDs. The PSU has already been eliminated as the culprit as it has been swapped out, but the fault remains, therefore the mainboard is the suspect here.
:grinthumb