carfax does recieve info from insurance companies (however, not ALL of them)
there are still a few service/body/repair shops who do not report to carfax, so if a car was repaired there, it would not show up on the report, and if you look at the website in the Terms and conditions it even states:
NEITHER CARFAX, ITS AFFILIATES, NOR ANY OF THEIR RESPECTIVE EMPLOYEES, AGENTS, THIRD PARTY CONTENT PROVIDERS, OR LICENSORS WARRANT THAT THE SITE WILL BE UNINTERRUPTED OR ERROR FREE; NOR DO THEY MAKE ANY WARRANTY AS TO THE RESULTS THAT MAY BE OBTAINED FROM USE OF THE SITE, OR AS TO THE ACCURACY OR RELIABILITY OF ANY INFORMATION, SERVICE, OR MATERIALS PROVIDED THROUGH THE SITE.
Carfax purchases the info from third party vendors. all we do is compile it into a useful form.