It should be clear from the MEL item Tech Log entry whether it is a fault or a false indication - pilots do not decide that, engineers do. (Except in flight of course - confirm failure on SD/FAULT light before ECAM actions).
It's always the captain who decides how to treat the corresponding warning. Engineers might offer a option but it's always a commander who decides whether to accept it or not. All depends on the failure, the history as well as all the other pertaining factors.
