Again, you are entirely correct (and provide useful insight and education to those less aware of the intricacies of the beautiful game). 
Which is why I said ‘on the pitch’ knowing that someone would note that linesmen (or women) are today called assistant referees (they would perhaps be linespersons if we had not moved to assistant referees). But they are still ‘assistant referees’ not ‘the referee’ and are rarely on the pitch itself (the pitch being the field of play rather than the entire venue).
the linesmen/women and fourth official are assistant referees and will take over if the referee is injured
You could say that one of them would be parachuted in if the referee was unable to continue for any reason.
(I’d get my coat but it is currently being used as one of the goalposts - along with my jumper.)
