Perhaps the parent would try to find another activity that would be just as fun for the child. Maybe they would talk to one of the horse folks and ask if they could arrange a time later to get together. But the general idea that only children raised with rules in their households know how to follow rules outside of them, is just false. Like I've been saying, TCS parents share information with their children which includes information about what others might expect from them. The only difference is that the child is free to decide that the rule and therefore the activity is not important to them.
Every family there has definite rules and authority.
Since TCS is neither, I don't think this story is a refutation of TCS theory although perhaps you did not mean it to be. Yes, I would agree with this statement.