The statute of limitations on property damage and injury claims in Ohio is two years — so you are well within the time frame to file a claim. The car being keyed would count as an act of vandalism, so your comprehensive coverage should cover the damage.
Even if the vehicle you backed into was uninsured, it is still your responsibility to pay for the damages if you were at-fault. If the other party doesn't want to go through insurance, then they don't have to.
Insurance will not cover cosmetic damage to your vehicle — even with full coverage, insurance is meant to cover sudden and accidental damage. See the differences between collision and comprehensive coverage and what they cover here.
Unfortunately agreeing to pay for damage out of pocket without involving your insurance company can lead to issues like this. He does not have to agree with your offer and can attempt to get you to pay more than the actual cost of the repair.
If the scratch was the result of vandalism and not caused by another vehicle then filing a comprehensive claim should have little to no impact on your future rates. This also means that you will have to pay your comprehensive coverage deductible for the repair.