Ask for a note from the previous owner, forget about carfax, a note is what counts
Thinking about it that could make more sense, if there is faults then I'm pretty sure it's easier to sue an individual than carfax that probably have a heavy liability write-off disclaimer somewhere
A third option is to take the car to a mechanic and ask for a quick inspection, no car dealer would have anything against that unless there is problems with the car
