I'm not the parent, but IMO the end-user should be in control of the computation on a computer... and that concepts of "ownership" don't really apply to data. So when you say "their data", it is very unclear what that should mean.

I'm a copyright abolitionist, so I think when you write a book, you can only "own" that physical copy. When someone reads that book, the words in the sequence that they read them are now part of their memory and autonomy of thought. And so on.