Earlier quoted context omitted.
On a Windows account, a user can change the default browser for their own account. Therefore, a user can delegate the choice of default browser to the remote management. A user can record which sites their own browser visits. Therefore, a user can delegate that authority, allowing remote management to record which sites that user visits. A user does not have the authority to record which sites are visited by another…
>On a Windows account, a user can change the default browser for their own account. Not if they lock down that setting via GPO and let the default behavior of remote > local. There's a lot of settings that can't be undone in the GUI and take diving into the registry to undo when set by GPO but then they'll just get re-applied on GP refresh anyways. Talking about who can do what is immaterial to how domains and remote…
The parent owns the device and would have the local admin account. They aren't joining the device to a managed domain where something like GPO would be relevant (unless configured by the parent, naturally). The student would only have a non-admin local account, and would be incapable of granting device administration privileges to the school. The school could still manage their browser profile, of course—if the browser itself is actually signed in to the school account, which is something you can disable while still logging in to the account on the web—but they would have no access to or control over other user accounts or anything else requiring local admin privileges.