Inertia is intrinsic property of a body by virtue of its mass. From Newton's first law, a body tends to be in state of rest or motion, unless an external unbalanced force acts on it. Thus, to pull out table cloth from under the dishes and silverware without disturbing it, external pull force is applied only on the table cloth and the dishes and silverware do not move due to their inertia of rest.
In this case where we have find he moment of inertia of this object about an axis perpendicular to the x-y plane and passing through the origin, we can just add three moment of inertia's .
