Yes, quality is recognizable in both Europe and America

An indicator of how relaxed a horse is performing at liberty is the side checks/check reins. A loose check indicates a horse relaxed and staying off the bit. Although people think the side checks keep them straight and looking ahead a comfortable responsive horse will relax his neck muscles, back off of the bit, and turn his head to look at the trainer for direction and guidance. A tight side check indicates a hard mouth, one in which the bars have become so insensitive that they lean or push on the bit in an effort to escape the confinement of the checks, the surcingle, and crupper.
Kathy Carden's liberty horses were really nice Polish Arabians. I believe a couple of them traced to Lasma's immortal, Bask.