correct. But it's harder to stay in sync with your horse if you are not over your own legs and close to his center of gravity, and your upper body lagging behind your lower body.
Well, if you look like this, I agree
However, if you are using any standard approach to riding, then I have to disagree. Riding in an English jump saddle with a position close to a 1900 cowboy (although a relaxed leg), it was EASIER to stay in synch with the horse's motion. Very few people have the flexibility in their back and strength in their tummy to absorb that motion completely with their back.
And if I lean forward, light in the seat and my weight centered over the stirrup bars/withers, then I am centered over the part of the horse that moves the least, and I have very little motion to match at all! The dressage seat, IMHO, is the hardest seat to ride well.
And if the horse is moving fast, the "classical seat" has your center of gravity farther from the horse's than the 'classical western seat', since moving your legs forward moves your center of gravity forward too! The dressage seat is designed for dressage, which values collected gaits. Collection moves the horse's center of gravity back, and that makes it somewhat easier - but you are still trying to absorb the motion of the horse with a part of your body not designed to compress vertically: your spine.
Any rider should lead his horse's motion. If you want him to shift his balance to the rear, then you ought to do so first and give him a reason to shift too. If you want your horse to slow, lagging the motion with your rump gives him incentive to slow. That has nothing to do with what seat you prefer. That is Riding 102.