What you're describing, combined with the sort of state provided access being described, seems like it would incentivize the child learning how to lie and hide things more effectively. It's absurd that the school would facilitate such broad and directionless access to the internet outside of the parent's supervision. It's directly undermining them.
And how's the parent punishing them not incentivizing the same behaviour of lying and hiding more effectively? If you want something done on all levels, you need regulation on all levels - any hole will be exploited, and kids don't have such a thing as "responsibility" developed yet.