In a civilized society, a call to the rental shop owner and the insurance would be around to sort things out. That is why you pay the deposit after all.
Unfortunately this is not a civilized society and so the tuk-tuk owner will feel free to demand the first exorbitant amount that comes to mind, and back it up with the threat of violence by the crowd of AN posters, I mean Thai thugs waiting for a sign for the beatings to commence.
Anyone who believes a civilized negotiation was possible in this scenario has never been to Thailand before.
And, of course, the police will all be snuggled away in bed despite the frequency of such events.