When i passed my test i was a student and couldn't afford normal insurance just like most young drivers the idea of a blackbox is to encourage safe driving while almost halving your insurance cost i think for no box on my first car was £2300 without was around £1550 so i went for the box, all well and good saying don't get a box its more about can they afford the extra grand or whatever it will be extra.
I might be wrong but i'm assuming your parents are buying you the car or insurance or both? if so of course its their right to pick what insurance you get....what you going say stick your car because THEY wont pay an extra thousand for you not to have a box? if you're the one paying for it then no they cant force you to get a box or just tell them you bought box insurance how would they know? they going to sit looking out window looking for box installation people turning up?
Don't get me wrong i'm no way supporting a black box they're ****, made me want to quit driving like literally first year i had it i must of done probably 400 mile as all i thought about wasn't the road but what clown is going to lower my score and dreading checking the app but in some cases there really isn't much of a choice all you can do is drive like a granny for a year lol. If the problem isn't your parents paying for things then simply buy non box insurance but tell them you did as there really isn't anyway they will know, if they ask where the box is just say its coming then wait until they go out then make out it came and you've fitted it like it isn't hard to BS it, still wondering why you even need to have a box if your parents aren't the ones paying.