I am not a saddleseat rider myself, but I have an open mind to look at all the facts and hear from people in the "business" first before I cement my opinions.
Here are some pictures of a saddleseat saddle on the horses back to compare with a western saddle. (these have been hard to find btw and may not be as accurate a comparison as I would like so if someone in saddleseat would be able to post a pic of just the saddle on the horse girthed up from the same angle as one western one that would be great)
Not how both seems to go very far back on the horses back.
The lady in the OPs link has a VERY solid seat, her legs barely move whilst she posts and her hands are very independent of her seat as a constant contact is maintained.
Yes her hands are high, but so is the headset of the horse, if her hands were lower she would have broken the straight line from elbow to bit, as shown in these photos.
I believe the second picture also shows the saddle placement more, if it was further forward it would be impeding the horses shoulder action quite dramatically.
These horses really know how to use their shoulders and they do, having the seat further back than what you would see an english rider doing allows the horse to show off his full ability, which is what showing, in essence should boil down to, showing off the horses natural talent. These are horses which have been bred for the flamboyant movement and do so naturally, as shown by the video of the 2 year old gelding.
(thank you google for the images)