Your link didn’t work. I’m guessing you’re talking about up and down hills. Your instinct is correct but I’m pasting below some advice from Jessica Jahiel (author, clinician) that specifically answers your question. She has a great website with archived Q&As on a variety of questions. Site is http://http://www.horse-sense.org This question was specifically about best rider position(s) when trail riding in different terrain.
From Jessica: "There are times to sit, and times to get your seat up and off your horse’s back. If your trails are fairly flat, you’ll be sitting most of the time. If your trails are hilly, you will probably spend a good bit of your time in a half-seat (two-point position). Either way, it’s good to know what will make life easier for your horse.
"Up and down hills: The horse is a rear-engined animal that uses its head and neck to help itself balance. If you keep this in mind, you won’t make many mistakes on hills. Give the horse its head, as much as you possibly can, so that it can balance itself while it’s climbing and descending. Don’t try to make any big movements or any significant changes to your own position DURING an ascent or descent. To free the horse’s back and let its hindquarters (the engine) work effectively, you’ll do best to stay very slightly out of your saddle and balanced over your feet no matter whether you’re going uphill or downhill. Take your hills straight! Coming down at an angle can cause a horse to fall. To stay balanced coming down a slope, a horse needs to keep its hindquarters directly behind the rest of its body, not off at an angle. When you’re coming down a hill and you are MOST tempted to choke up on the reins and look down, don’t - instead, let the horse have a little MORE rein, and keep looking UP. It will help both of you stay balanced.
“Going uphill, don’t hesitate to get into a half-seat, give the horse a long rein, and let the horse do the work. Sitting and kicking just makes the horse’s job harder. Horses can canter up hills more easily than they can walk or trot, so keep that in mind. If your horse offers a canter up a steep hill, don’t panic and assume that he’s running away - he may just not have the strength required to trot uphill.”
Hope that helps!