3 years ago, I accidentally backed my truck into someone's 6 month old car. I left a note, and the lady called me. I offered to settle outside of insurance. SHe came back to me with a price of over $6000.00. Urk!! I then decided to put it through the insurance. The payout was $3600, so I guess she was trying me on for size.
I suppose though, that I should have paid it. The premium on the truck went up by over $2000/year, so I've already paid that much out just in increased premiums, and my broker tells me it will be like that for another 2 years.
What's the point of insurance if you have to cover twice the loss anyway?

If I were to do the same thing again, yes, I would own up to it, but I might at least briefly think twice about it.