What is that?
I don’t think it is as much a mystery as implied.
In the end there’s no getting around that mixing device uses like this doesn’t work. It works less and less as the history of computers goes on.
Because, if yes, this absolutely does sound like a security hole:
1) Set up an organisation and add a managed account. Set up policies that install a backdoor on first login.
2) Get hold of victim's Chromebook.
3) Log into the Chromebook using the account from (1)
4) Chromebook will execute the policies and run the backdoor.
5) Use the backdoor to snoop victim's files.
You've successfully gained access to the victim's files without knowing their password. Profit!
This would work even if the victim is fully aware of the issue and never intended to mix managed and unmanaged accounts on their own.
The first user to sign in on a chromebook has limited special powers. I don't think they involve reading other people's data though.
Surely this is the entire value proposition of ChromeOS - you sign in to your account, and the laptop magically becomes yours? It seems like a serious hole if a single sign-in is able to compromise other accounts.
Students don't get to decide what software to install when it comes to logging in to school accounts. Generally the laptops are provided by the district, but it seems OP was trying to add another personal device to their system.
You can't participate in their system without the software. So I guess the alternative would be to block personal devices from logging in like this at all.