Yup, I can't see why they even bothered to inspect her car. It's not like they have ever covered her car in any way.
Thats not unusual. Even in liability only situations, the insurer will still want to photo the car of the insured to a) Have a record of it and b) For comparison purposes (i.e. to make sure the damage that the 3rd party is claiming matches up with the other vehicle). Never heard of an insurance company having authority to total a car that they don't even cover. That doesn't sound right to me.
I would gamble and buy a salvaged car for a smaller amount, say < $5000 for a car that is originally worth $15-20K but I wouldn't spend $13k for one that is worth 30, 40k, too much risk.
Over on Rankin Rd.? I thought that one was called Metro Auto Auction, but they might have changed names. Big H Auto Auction has a ton also. Both at both places, you might have trouble getting in without a dealer license.