I don’t believe you are correct, as
@Coulomb has said, as RCBO will trip on overload as well as earth leak, but not an RCD.
An RCD has a max current rating (eg 63/80/100amps) that it will work correctly up to, if this was/has been exceeded then it may be damaged and not work properly.
It does worry me that something else is wrong with your house wiring, wouldn’t want anything bad to happen. Your choice obviously, but I think I’d be tempted to replace the RCD to be on the safe side incase it is damaged - quick/cheap/easy to do.