If they're paying on their insurance, then there is no benefit to your daughter at all. After all ,they'll be telling their insurance what has happened, which means that the incident will be recorded, and your daughter will have to tell her insurance that the incident happened (as per terms of the insurance, failure to tell is fraud). In which case her premiums will still rise next year, whether or not she makes a claim, whether or not the car was parked and the other party was at fault.
The only way in which she is better off is if they pay for it DIRECTLY. No claim involved on their insurance. Of course, she still should inform her insurance of this fact (which would push up her premiums), but it's entirely understandable if she 'forgets' to do so.
If it was my child, I'd 'encourage' the other party to pay without speaking to their insurance at all. Though that depends on the damage to their car, of course. If a claim has to be made (by either party), then your daughter also needs to make a claim, ensuring that she also claims for any increase in premiums in future years : her insurance co. should be able to help with this risk pricing increase.
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