While Carfax reports are generally good they are not the sine qua non they are purported to be.
I had a major accident in Pennsylvania with my Tundra pickup - to the tune of $16K to repair. A year later I traded it in. I got a look at the Carfax report the dealer pulled and it did not show the accident or damage report.
Six months later I was looking for another car to replace another vehicle and bought a Carfax package. After settling on the car I wanted, I used one of the other reports to look up the truck. It was now in North Carolina, with a new owner and still without a report on the accident.
By all means, use Carfax, but just keep in mind their system is only as good as the reports they receive.
Caveat emptor.