And a kitchen/kitchen corner. I think what the parent is suggesting is that apartments wouldn't have kitchens at all, and you would eat at communal cafeteria. I believe this is what the vast majority of city dwellers in imperial rome would do?
Y'know how, in old movies, single people would live in single-room apartments, often with a Murphy bed that played a part in some amount of slapstick humor? They weren't cooking in there - dinner was served downstairs.
Yes -- boarding houses. It was expected that your rent would include at least an evening meal shared with the other residents. And like with many university dorms today, it was against the rules to cook in your rooms.