Hi Bob, if it was just the surface that was discoloured, and you have been to see it now...Would you be recommending she invest's in an extractor fan for the shower area, as you said in your OP.
Suspect it could have been created by the atmospheric moisture cloud you get in a room whilst showering? After all, that contains dirt too, that will condense onto the tile face at the top of the room, and run down into the grout joints.
I thought air extraction is a requirement for shower-rooms in new-builds thesedays, to comply with ventilation regulations.
I always recommend it to all my customers if they don't have one already, and if possible on a timer for about 10-15 mins afterwards.