Sure you aren't breaking Arkansaw law Wil36 by not reporting this accident? I believe you would be in some states.
It's a misnomer to say accidents get reported directly to carfax. They get reported by law enforcement when law enforcement is involved--or they get reported by states requiring dealer and auto repair folks (like Wil36) to report accidents--or by insurance companies. Basically the accident gets attached to the title--we call it a "salvage title" here--or it gets reported to the state who maintains records of accidents. Both sources are checked by Carfax and others. But that's not the end of it--a lot of other useful recorded info--such as maintenance history with dates and odometer readings from dealer shops, title history, non-accident damage (e.g. flood damage) that is recorded by the insurance company-- is collected.
But of course not every accident gets reported. Sometime even when it is required to be by law. Carfax, autocheck--and there are a couple of others--are only as good as the info available to them for that vehicle. They can't be held responsible if people are required to report an accident to the state--but do not.
I've seen several critical comparisons of which is best and they all indicate carfax is the best by a hair--also the most expensive to check into on your own.
Bottom line is they aren't perfect--but they do help catch quite a few problems you'd have no idea about even if you inspect the car thoroughly!
See here for an objective take: http://www.edmunds.com/car-buying/wh...t-for-you.html