Liberty Riding is a wonderful way to demonstrate the relationship between you and your horse and showcase the abilities you both possess
it does not demonstrate anything more than how well trained a horse is. People I think see alec and the black stallion, where their "magical bond" allowed alec to control the horse(an extremely unruly, forward, and sometimes dangerous stallion) by just asking.
In reality, it is a horse that is well trained to work off seat and legs. Horse and human relationships are great, but its a lot of training and hard work that gets a horse to do as its asked, when its asked, with minimal tack. My BO has a mare she adores, that likes her, but she doesn't work off seat or legs. Put her on said mare bareback and bridle less, and they would be running aimlessly all over the arena. It doesn't matter how many thousands of miles they've gone together, or how much mutual trust and respect they have.
Liberty ground work can be a good tool for people, helping them to stop relying on the halter and lead and more on body language, and it can be a way to increase trust and understanding between horse and handler.