I think CarFax accidents come primarily from police reports and other "public" records? Do insurance companies submit none, some or all of their data to CarFax? If the insurance companies don't submit, there could be a lot of non-police reported accidents that don't show up, including floods, etc.
Here's what they say:
Our unique database contains more than three billion records. We receive information from thousands of public and private sources including all Departments of Motor Vehicles (DMVs) in the United States and Canada, as well as many vehicle inspection stations, auto auctions, fleet management and rental agencies, automobile manufacturers, and fire and police departments.
The exclusive CARFAX Buyback Guarantee reduces the risk involved in buying a used car. If CARFAX fails to include a DMV-reported incident (salvage, fire, flood damage, odometer problems, lemon history) in a CARFAX Report, we may buy the vehicle back for the full purchase price.