anytime i see 'carfax', it reminds me of this:
https://abcnews.go.com/Business/trus...8#.UbOr4_nrxyU
it's typical sensationalist crappy journalism, but the main takeaway is that carfax is a aggregate of vehicle information. there is no law requiring anyone to report anything to them, just as there's no requirement that they need to collect anything. the sole drive they have is to collect your money from looking up any specific vin.
so while i still always do carfax's on vehicles that i'm serious about, i still highly recommend either training yourself to look for signs of damage, or taking it to an experienced auto body guy and/or mechanic to be inspected.
personal story-- i bought a 2001 eclipse around 2008, at the time where carfax was heavily pushing it's services. the dealer shoved the clean carfax in my face, appearing to show the entire registration history of the car with no accidents and i bought it, no other questions asked. a year later after an accident, i took it to a family friends body shop for the repair, and within 5 minutes of pulling it in, he showed me how it was rear-ended hard enough to tweak the door alignment, some rear wheel well overspray, and the parts that they had replaced and tweaked in the trunk area.
TLDR: carfax is good to check, but trust it like a used car salesman--re-check yourself, and never trust only in what the report says.