Carfax is just one layer of due diligence. I hear people all the time talking about taking a car to a mechanic for an inspection. I wonder how much it costs to take a car to a reputable auto/body shop for an inspection to determine previous damage/repairs.
I lost complete confidence in CarFax years ago after this one: My wife's car was hit by a driver that fell asleep and drifted into her lane (traveling same direction). The accident was recorded by the police department, both parties had insurance policies by nationally-known providers, and her car was repaired at a Ford dealership. The repair was in excess of $2500
All that, and nothing ever showed up on CarFax.