And please know that the whole US airport / airline culture is imbued with such a sense of self righteousness and officiousness - you wonder if they realise they're running a business for paying customers, because they act as though they're doing you a huge favour.
Yes they are, I fly out of the US a lot, however, there has to be some level of 'fear' to keep people 'in line'. You have a limited number of staff trying to control a couple of hundred people in a tin can flying in the air. If the threat of such heavy handedness keeps me and my family safe on a flight, I welcome it.
To my mind, describing scratching, especially when the girl isn't sitting next to other passengers but her parents, isn't a good reason to land the plane.
The airline did not know whether she would stay in her seat. She could also scratch the passenger in front of her, flail about and hurt herself and the passenger in front of her. Its about risk management.