Do not turn it into your insurance, if you do, then YOU started the claim and the damages will count against you. If going through insurance, you need for him to turn it into his insurance.
You were hit in the rear, he can change his story but you were rear ended… he will end up having to pay.
If the damages are light then out of pocket is fine. Its the bigger hits that its a PITA… like if you went to get an estimate and it was $1300 and he says sure, that’s fine… then you take it in and your final bill is over $2000 because of hidden damage… then you have to chase him down for the difference, etc… That’s only on really big hits tho. Take it to a quality shop and get an estimate, ask the estimator if he thinks there will be any hidden damage because someone is going to be paying out of their pocket to fix the car and you need a fairly solid number.
If the estimator says, Im not sure, there might be hidden damage, then tell the guy that hit you, that you want to go through his insurance because there might be hidden damage and you want to make sure the body shop gets paid in full so that you are not stuck with a bill.
Make sure you get the money up front from the guy.