This is exactly the thing I was trying to say in the beginning about a teenager seeing things differently than an adult.
Her comment about " it only stepped back a half a foot or so",
The OP says "she has no issue with her horse moving because it gets tired or needs to regain its balance, if its moving around a firm growl or a quick jerk on the halter."
She looks at the handler telling the horse in no uncertain tems " don't move" Obviously the horse moved and pulled out the cord and then the handler made her corrections. In her opinion as stated above, she has no issue with her horse moving a bit. Well, maybe this handler did not want this horse to move at all.......
Moving a half foot when supposed to stand still could cause a vet to get hurt, a farrier to be stepped on or any number of issues.
I stand by my comments that the teenager saw what she saw, decided it did not agree by her standards of how she makes her horse mind and felt she needed to report the lady for abuse to the barn owner.
When the OP's horse takes advantage of her letting it move a bit to regain balance or because its tired, and breaks her foot, or breaks the farriers foot , then she might understand that although the handler corrected her horse how she wanted to, the OP has no right to report a training correction that she knows nothing about, except it was mean to the poor horsie.