Hibernating is turning it off, the difference is that it restores the state of the OS instead of having to boot from scratch. Standby puts the machine into a low power consumption state. Hibernation is superior to standby for power savings and equal to shutting it off. And in my experience, standby isn't very reliable (usually forced to do a clean boot when it fails on start up), and resuming from hibernation is much faster than a clean boot.

You are right about taking action while having only a limited understanding can cause more problems. However, the "action" people want to take here is to stop doing things and leave nature as it is rather than keep marching along with progress.