That risk is managed through medical certification. The real problem with understaffing is that one person can't handle all that work.

"Funny" enough if this controller had had a medical emergency (or just bad sushi) and been off the radios, this wouldn't have happened because the fire truck would not have received clearance to cross the runway and wouldn't have. Or at least would have crossed like the airport was uncontrolled, been much more careful and announced itself, and likely have seen the landing aircraft.