Man, I must be way too trusting, because I would not rule out letting the guy's cousin fix it. I don't see any harm in letting him try, and if it's not done to your satisfaction, then hold him responsible for fixing it satisfactorily. You could discuss this up front, and even get it in writing. Then the cousin has incentive to do the job right. As long as this guy has demonstrated he is insured, I don't see why his insurance company would care either way. Whether they have to pay to fix it now, or after the cousin has tried but failed, I see no difference. Not everyone is a shyster, and there was a time when people would solve things on a handshake. Take pictures beforehand, and the job is not done well, it will be evident.
And look at it another way: If an MMM devotee who is really capable at body work rear-ended someone accidentally and in their DIY spirit of frugality asked to let them fix it rather than going to an overpriced body shop, wouldn't it be unfortunate to just be told, "Nah, I'm taking it to the overpriced body shop?"