An excerpt from my memory: "In the locker room, climb the ladder leading to the ledge where the cloth is located, touch the cloth, then climb back down the ladder and climb the opposite side ladder to reach the other ledge. From there, climb the broken top floor piece to reach what's remain of that original top floor..." I'll say there's more easy way to do that

Once you touched the said cloth just run-jump on that broken top floor piece then you just need to keep run-jumping until you reach the top floor. So the writter of such walkthrough was option 1 not aware of that or option 2 unable to do it because of the behaviour of the game at that time. (talking of Gahreesen in that paragraph)
I think many explorers are just afraid and don't exploit some little stuff. In Gira, for example, it amazes me to read explorers saying, I'm reaching (hardly?!?) the vent in the middle of the lava stream then (exhausted?!?) by this (awesomely hard?!?) jump, I link out and return after.