You have to treat the carfax report as a major red flag. Minor accidents (and in my experience, many major ones) are not reported to carfax. But that does not mean that carfax is worthless - far from it.
Ask to see the title. When a car is totalled, the insurance company pays it off and the car is auctioned for salvage or scrap. Some of these cars are then rebuilt using cheap or used parts. Most, but not all, states require such rebuilt wrecks to have a title "branded" as "salvage". But some states do not have that requirement and dishonest sellers can "wash" a title by transferring it through such states. So a title branded "salvage" = rebuilt wreck, but a seemingly clean title doesn't necessarily mean its clean.
The beauty of carfax is that the report follows the VIN forever and cannot be laundered. The carfax may also show the paper trail across state lines. But, because so few accidents are reported to carfax, there is no substitute for a thorough pre-purchase inspection by a mechanic for any used car.