I train my own son, and a few kids of friends. I have zero interest in doing it otherwise. That said, what you observed is commonplace. My POV about most "TMA" doing that, is that it is a mistake. My mantra for it - "The first way is the worst way." I have had some long debates IRL and in stand up forums with traditionalists over it. E.G. some styles of karate, and especially Shotokan, teach kihon/basics for kicking by having you keep your arms out to the side and low. I understand very well why they do it, I just do not agree.
It is as though they treat everyone as being mentally challenged when they start the system. One of the things I love about boxing, is that every coach I've met, teach the correct fundamentals from the first session. There are no baby steps, no "building up to it", you learn correctly from the get go. Hence, no built in bad habits to unlearn later.
The girl is excellent, and pop is training her great. And he was doubtless trying to show off how coordinated she is already. I just like to nit pick, because I am an asshole like that. :|