No big deal!

1. First for parking lot accidents, it's hard to judge who is at fault and usually both at fault.  Insurance companies will treat both at fault though one party may even have witness cliaming the other party is at fault.  It really does not matter who is at fault.  It's a small accident after all;

2. Even you file the claim, insurance raise will be very minimal and may not at all.  Many insurance companies have a forgiveness policy meaning they will forgive one accident every a few like 3-5 years for small accidents less than $750.  So don't worry it too much.  Even though you got insurance primiun raise, it still worth it since it's a protection for future unexpected bodily injury.  Also, this is what your insurance for: protecting your property damages and perosnal injuries;

3. I guess the reason the guy insists going with insurance companies is because he finds it's kind of hard to work with you so he changed his mind and decides to go with insurance companies to protect himself in case you file claims for future bodily injury. 

All in all, the best way is still going with insurance though sometimes it does not have any monetary benefit due to deductables assuming your insurance pays you and his insurance pays him.  You worried too much!  Relax, rest and let insurance companies to deal each other.