I got rear-ended in traffic about 20 years ago, just as I was about to trade in the car. I was advised by some contacts in the trade that it wasn't a great idea to bring a recently repaired car for trade-in, as they would be assuming the worst in terms of the damage.
So having explained this to the insurance company, they were quite happy to pay me for the full value of the damage claim, less VAT and car hire (as these were not actually incurred).
I think the young man has got off lightly, and if had any sense, he would be keeping his head down. He might have a slight quibble about paying for car hire that didn't take place, but €300 for any car damage is peanuts. If he calls again, the OP should tell him that she is getting a 'main dealer' quote for the damage and will be approaching his insurance company to cover the cost of the claim, less the €300 already paid over. That might soften his cough.