When I purchased the 2009 Honda Pilot, The car fax did not not have on it, that there was a problem with the transmission
How would carfax know?
Besides, that’s not the kind of things carfax keeps track of,
The mechanic you paid to do a pre-purchase inspection should have found it though.
Carfax only can list what was reported to them, they do not have a crystal ball, nor employ soothsayers to predict future problems.
Eleven year old used car is always a gamble.