Typically, a not-at-fault claim won't effect your rates. Even if you can't prove it, it should be classified as a hit and run. You'll have to pay your deductible, Geico covers the rest and everyone moves on. Personally, I wouldn't trust someone flagging me down in a parking lot compared to a body shop. If he has a legit business name, shop, etc, then you could go through him, save a few hundred bucks compared to paying your deductible. Just be aware that once he starts messing with it, it'll be hard to get geico to cover it later on.