The video doesn't make sense. For example, in her martial arts demo, she was pushed sideways. Most riders don't experience a lot of sideward pressure. Instead, it is fore-aft. Horses accelerate, or stop, or jump - and the pressure is front-back, not side-side.
Next, it looks at a rider on a horse that isn't moving. Riding isn't about sitting on a motionless horse. It is about getting our balance and motion to go in synch with the horse's motion and balance.
When they moved at very slow and a predictable pace, the rider faked the response. I've stopped Mia many times with legs forward and saying "Easy" - and she does it effortlessly. Without using the reins, and without any tension. It is, after all, how she was trained to stop.
If you are riding a bus and it is about to come to a fast stop, do you make sure you have shoulder - hip - heels aligned, or do you stick a foot forward and lean back? Everyone I see takes door #2, because it prevents you from sliding forward.
In dressage, the seat is not supposed to be forward. After all, a collected gait isn't meant to be fast, and the horse is not supposed to be making any unplanned and sudden stops during a dressage test. However, the horse's balance point is roughly at the withers, and a forward seat shouldn't have your rump down in the saddle.
For western, the saddle is designed differently. The tree extends well beyond the cantle, and the way you have even pressure on the horse's back is to have your balance point at the saddle's middle. While you can do that with shoulder-hip-heel aligned, you can also do it with feet somewhat forward and be ready to lean back a bit in a stop - or forward to go fast.
There is nothing inherently wrong in riding with shoulder-hip-heel aligned. If your goal is a collected pace, or if you want your horse to pivot, then it is very helpful. For trail riding in a western saddle, or reining, or cutting or some other activities, it is not. It is not right in a forward seat, since you fold up - thus putting your hips slightly behind, and your shoulders slightly forward. At extremes, the folding creates this:
You will notice that Gen Patton does NOT have his heels, hip and shoulder aligned, nor should he for what he was doing.
How one should ride depends on the horse, the tack, and your goals for that day. It most certainly CAN mean keeping shoulder-hip-heel aligned vertically, but it does not require that at all times.
This would be pee-poor riding for dressage or jumping, but works for cutting:
I dislike the use of the word "unmovable" - I have always been taught to flow with the horse and be fluid with their movements. I was sort of confused by the dancing analogy at the end with the "unmovable" mantra.
I agree with bsms in that having the horse standing still and Erica Poseley on the ground was really not helpful. It won't really help prepare you for when the horse is moving. I also agree with your signature, bsms - it summarizes what I have been taught (and have begun to teach) perfectly:)! I don't think the best and most effective way is necessarily the prettiest, or "correct" way all of the time.