"They can do it for their teacher"

Here's the observation that seems to settle it. At school, Sam remembers things. He sits still. He's ready for PE. His teacher says he's lovely. So he can, and he chooses not to at home, and that's a choice about you.

Go back to Munakata's transitions in chapter 4. The first was learning to override a habit in response to signals from the environment, and the third was moving from environmental signals to being self-directed. A classroom is, from a child's point of view, one long environmental signal. The bell. The timetable on the wall. Thirty children doing the same thing at the same time. A teacher whose whole job is cueing, who says "pencils down" and "line up" and "PE kit on your peg" at the same moment every day, to everyone at once. A child in a classroom is a child being cued from every direction, and a nine-year-old with reactive control can do a great deal in that setting.

Home isn't like that. Home has one adult doing eleven things, a tablet, a brother, the television, no bell, and a request that arrives once, from the kitchen, while something more interesting is happening. The setting has none of the cues, and so it asks for the self-directed control that the classroom never needed, and the child hasn't got it yet, and you conclude that the difference is attitude, when the difference is the room.

The teacher's report isn't evidence against the child. It's evidence for the arrangement. It tells you that with enough cues, your nine-year-old does everything you want, and that's the most useful thing you could know, because cues are buildable, and chapter 19 is a description of how to build at home a fraction of what the classroom does by default.

There's a version of this that's about respect, that Sam does it for the teacher because he respects her and not you. I'd only say that respect isn't what makes a child line up when the bell goes. The bell does. And the teacher, if you asked her, would tell you that the same children who are lovely in her room are exactly the ones whose parents say "you'd never know it at home", and she'd tell you that it's every child, and that the difference is her room.