About 8y ago we were looking at a used Mini Cooper. Car Fax reported no major problems. I went to the bank to get a loan. They reported 2 minor and 1 major accident that the car had been in that were NOT reported by Car Fax. Once we knew where to look we were able to see evidence of the damage & repairs to the car.
I think that if lending institutions don't trust Car Fax then we probably shouldn't either.