What you find listed in Carfax is questionable. What you don’t find in Car fax is totally meaningless.
Of all the cars I have owned since 1965, not one of the is going to show any maintenance, except maybe on brake job while I owned it. Unless the owner went to the dealer for service I doubt if Carfax is going to have a record of it.
While a lot of people live by it, I would not bother with Carfax myself.