Spog, is your vehicle insured with the same company as theirs?
It sounds like they are claiming the whole cost of repairs, rather than an excess. Is that right?
** I HAVE HAD EXPERIENCE IN SOME FIELDS WHICH LEAD ME TO WRITE THE FOLLOWING. SOME OF IT IS COMMON SENSE, SOME IS PLAIN FACT, SOME IS PERSONAL OPINION. YOUR CHOICES AND/OR ACTIONS SHOULD BE WELL CONSIDERED AND NOT BASED SOLELY (IF AT ALL) ON MY POST **
Firstly, I would DEFINITELY keep all correspondence and write down 'verbatim' or as close to it, all spoken interactions, along with time, date and contact number of other party.
I would invite them (insurance company/ies) to prove your daughter did the damage. Hell, invite them to prove she was even there on the day. Sure, she left a note, but anybody could have written that. Sure, she sent emails stating she caused minor damage, but none of that proves she created the damage being claimed.
I would presume the insurance company would have expected a Police report for the "extensive damage" done, particularly if there were 'witnesses or CCTV'. I'd ask for the reference (event) number so you can chase it up. It should list your daughter and her car in the report if any of this crap has in fact been reported to the Police. If not, less ground for them to stand on.
Ask the insurer if they can outline the details for their mandatory Internal Review Process, and their mandatory External Review Process, or if you should simply bypass them both and take your complaint direct to the Australian Securities and Investment Commission. Might not hurt to mention the Financial Services Ombudsman either, just to make it sound complete. (And no harm in starting to ask about your options with these agencies anyway).
Also I'd ask if the "repairer" who wrote the "quote", would be willing to front these agencies and say that the damage was even "possibly" caused by the same incident, let alone "probably", let alone "definitely", (which nobody could say anyway). Remember that each different incident warrants a different claim (and therefore another excess). Hence the reason these grubs are trying to get it repaired at your daughter's cost.
At the end of the day, there is no Police (at least NSW) action likely to be taken due to the statute of limitations. They couldn't prove beyond a reasonable doubt that your daughter caused ALL the damage anyway.
As far as any civil claim goes, these teeter on the balance of probabilities, meaning the onus is to prove that it "most likely happened", rather than "it ******* did happen". From the information given, any magistrate should be expected to have enough common sense to see straight through this ********.
If it were me, I'd stand my ground and let them prove their ******** story, rather than give in as the little guy.