There have been occasions when an FI has been on board purely as a passenger when an incident /accident has occured and the FI had to take some of the blame even though they were not PIC!
The thinking is that the FI is likely to be far more experienced and should be monitoring what is happening and should intervene if necessary.
Personally I think this is a load of b*lls. The person in charge is always the PIC no matter if the passenger is Chuck Yeager! (Mind you I'd ask for help if he was there!)