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>Windows can wake itself from hibernate.

You're confusing that with sleep. Windows can't wake itself from hibernate as the machine is fully powered off, not in some sleep state.

No, he's right. Windows can wake the computer from total shut down even (S5). It uses RTC alarms: https://en.wikipedia.org/wiki/Real-time_clock_alarm

"Can be set to wake up" doesn't mean "will wake up".

Modern versions wake up out of the box, you need to tinker with them to stop that.