I suspect that most people claiming their horse is a certain height have never stick-measured any horse in their life. Most horse people don’t have a stick. And wouldn’t know how to use it if they did.
I also suspect that most people use the height they were told when they bought the horse. For horses they don’t own, someone says the horse is a particular height, and that’s the height.
Recently my friend was looking at a horse advertised as a well-built 16.1h. He was maybe 14.3, skinny, built like a feather. If a small child had sat on him and leaned to the side, he looked as if he would probably fall over. He looked as if it would injure him to have a full-grown adult sit on him. I have no idea how anyone could have believed he was in the remote neighborhood of 16h, much less well-built.