Just keep in mind that Carfax only reports the info they have received. Sounds like a no-brainer but not really since not everything is reported to them. Case in point, my 1995 Monte Carlo comes back perfect with Carfax. Though the car has never had any serious damage, it has been vandalized (repaint), had hail damage (repaired), and was involved in a collision. None of this shows on Carfax, but since I've owned the car since new, I know it all really did happen. But, since the authorities were never notified, all incidents were handled between me and my insurance company.
Carfax does give most info, but call your insurance agent. They can run the VIN to see if any claims have been filed against the car, regardless of company. I've done it with evey car I've thought of buying and have had one that returned a hit through my agent but not Carfax.