What I meant was how can the pas yisroel (and even the general kosher) status of the ovens, if this is an issue, be guaranteed over Shabbos. You have a goy with no neemanus using the ovens and he can sneak anything in when there is no mashgiach – assuming this is not a snack bar where they reheat wrapped food.
There is a chance that this may be a situation that is machshil es harabim, and also a chance it is not. It is unusual, that is for sure.