You should have paid already - you are completely liable. If they take you to court, you will lose.
Just think about the arguments you are making and others are on this thread and think about the common case of car 'accidents'. Accidents happen, but there are consequences for those who cause them.
i) The cause of the event is clear, although clearly wouldn't be taken any further, your DD assaulted their friend, and as a direct consequence of this the phone was damaged.
ii) Insurance is the choice of the phone owner and covers their mistakes - whether they have insurance and whether they claim is down to them. Even if they do claim on their insurance, the insurance company can claim again whose fault it is - i.e. your DD (and you).
iii) You don't get any say in how expensive an item you choose to cause damage to. Same way as if you hit a Ferrai, you can't say you shouldn't have such an expensive car - you are responsible for any damage you cause from an event you start if such damage is reasonably foreseeable.
iv) The friend does not have to use a case if they don't want to - they only have to do that if they want to minimise damage they cause - they don't have to do that before the accident - only minimise their loss after the accident.
v) They are entitled to a repair to get it into the same state - using original parts - and these must be carried out according to manufacturers standards - in essence, Apple authorised repairers must perform the repairs using Apple parts (otherwise Apple won't support it).
vi) It doesn't matter if they didn't have a tight grip on the phone as long as they wouldn't have dropped it anyway. If you crash into a car and the car then hits another, you are liable for the entire pile-up, not just the car you originally hit. There is no comeback by saying they should have left more space so if someone hit them they wouldn't have hit the other car.
If you said anything like you were not paying to me, I would rent another phone (of same type) and charge you for that as well - you are 100% liable and should have paid the same day.
Stop blaming the person who suffered the loss, and accept your DD caused the accident and is fully responsible. Pay up before they take your DD to court.