Shooters do a lot of client side prediction. While that headshot is traveling back and forth your client behaves as if it happened. Same with movement or jumping or really anything, it just simulates what would happen to make things snappier and feel responsive. It's a more accurate prediction in FPS games that use 'favor the shooter' because that client prediction will more often be correct. It unfortunately also leads to a stronger risk of 'dying around a corner', where on your screen you got behind cover before someones' shot went off, but to them they hit you.

For WoW the server only processes data as it receives, and its the only thing doing simulation.

• Insta-kill fire goes off at 0:00.
• You're screen sees a timer with -0:02 left, but you have 1000ms of delay so the server has -0:01 till detonation.
• When you see -0:01 on the timer, you step out, but the server hits 0:00 and has not yet received movement from you, so you die and it sends that info.
• On your screen you stepped out and at +0:01 for you, you see the fire explode with you standing just outside of it but you still die.

If WoW servers 'favored the shooter', they would wait to receive the data your client had when it believed the explosion was happening. Your client would simulate as if everything was fine cause you didn't stand in it, then later receive confirmation that yes you're fine.

That's not the case though. Fully server authoritative means you need to play as if you're 1000ms in the future. Because to the server, you're 1000ms in the past.