<human>: Can you give me a shortened version of the text?

Hey r/personalfinance

This is my first Reddit post & I was hoping I could seek some advice.

Finished my last class for the day & decided to fill up my gas tank at the Costco gas station near my house. There's a stop sign right before the Costco parking lot & I had two cars ahead of me, and two behind.
The car in front of me moved forward to take the place of the car that just had left & I moved forward as well, waiting to take my turn. The driver behind me was distracted & he rear ended me, causing what I think are minor damages. His car was undamaged.
We exchanged contact info, insurances, drivers licenses & pictures of the damage to my car. 

From there I don't know what to do. The person at fault is an Uber driver who's going through a divorce, has 2 children, and does not want to claim this to the insurance. He is WILLING to pay for the repairs to my bumper. 
I'm a college student & thankfully I have insurance, but i definitely can't afford out of pocket expenses.

Additional info that may help:
-I'm in the state of California; I don't know if this is a at-fault or no-fault state for auto accidents.
- I have Mercury Insurance.
- I have pictures of the damage if needed.
- I THINK the driver at fault doesn't have liability

What would be the best option for me? 
To claim the accident or to have him repair my damages? 
I really don't want my rates to go up for something I didn't cause. 

If you need any other info please let me know

Thanks for your time & help.
<bot>: got rear ended at a stop sign near Costco Gas. Have necessary info from other driver but he does not want me to claim it to the insurance company. He is willing to pay out of pocket.