they could have cleaned the area and the batter could have been dairy free and the risk of allergic reaction is still there
when you have allergies that severe having an epi-pen with you at all times is IMPERATIVE
any 'trace' can set people off if your allergy is severe enough
if the kitchen has other diary things going on the risk of getting a 'trace' in the food is there
my BIL's nephew couldn't even be in the same room as peanuts without having a reaction
it is up to the people with the allergy (and their parents for kids) to always be prepared
hell the dairy could have been on the table on the seat anything not necessarily in the food
but dairy is served there so the risk is there and you have to take precaution

this shit is similar to being a pedestrian and looking both ways regardless of if you have the right of way
because even if you have the right of way you can still get hit by a car
the driver of the car can be wrong as fuck but you still ran the fuck over because you didn't look both ways.