As has already been said, but in different words, carfax is only good for positives - i.e. if carfax shows a problem you can be pretty sure there is a problem. But a "clean" carfax report is useless and in no way means that the car is accident free.

Even problems that do get reported to the insurance companies may not show up. My wife drove her dodge neon across a bunch of those parking stops and ripped the undercarriage to pieces. (long, politically incorrect story)

Meanwhile State Farm did a piss-poor job of adjusting it and getting it fixed. Eventually it got to a driveable state but 18 months later the transmission just went to crap, you couldn't shift out of park at all.

She eventually sold it to a scrap yard as junk. 6 months later I did a carfax on the vin and it showed a clean record...

Funny story - she left it parked on the street for a couple of weeks with the busted transmission while she tried to figure out what to do with it. One day she woke up and it was gone. Turns out that the cops got a call that her car was idling unattended in the middle of the night and came and towed it away. Apparently a thief had noticed its long stay in the same parking place and thought he could steal it. You can just imagine his frustration after breaking in (a nice professional job too, only cracked the lock, it wasn't even visible) and then hotwiring the car only to try to shift into drive and not be able to move the lever! Now if only the police had called her, since she was just 50 yards away and two stories up instead of towing it, things would have been a lot simpler...