Deleting an object can suggest a broad scope in some contexts, but the proposition that every omission logically implies universality is false. If a particular person is already under discussion, the omitted object may refer to that person. In a general invitation, by contrast, naming no recipient may be consistent with broad address.
Resolution: ellipsis itself establishes only that the object is unexpressed. Whether it conveys a specific referent, a broad group, or tactful concealment depends on the context. Two utterances with the same surface omission need not have the same rhetoric.