It definitely appears to be entering hibernate mode. Under Power Options Properties, Advanced, I have Hibernate selected when I press the power button.

I press the power button momentarily, and it does appear to enter hibernate mode. It takes a good while for it to wakeup.. But mouse movement, a key-press on the keyboard, or pressing the power button again will wake it up. Windows ME does not give the option to disable wakeup via mouse or keyboard activity.

It saves everything I had going prior to hibernate, just as explained on the link you posted, and it for sure does take longer with hibernate selected VS Stand By mode when it wakes up. Am i missing something?