That’s not exactly what is meant, to just “pop in.”
The reason for the 2nd time being at Mass is because a person might attend 2 Masses on the same day. The Church permits someone to receive at both Masses. Clear enough.
On the other hand, someone might attend a Communion service only. That Catholic person can licitly be admitted to receive Communion. Not just a lay-led service either. Even a priest can lead a Communion service (but not as a substitute for Sunday Mass). Now, if that person later attends a full Mass that same day, the mind of the Church is that receiving at Mass is better. Therefore the 2nd Communion is permitted. And you’re right. Before 1983 that was not permitted (but there were some exceptions)
Another scenario: someone attends a Mass and receives at that Mass. Later the same day, the same person attends a Communion service (the reason is immaterial). That person is not eligible to receive. Why? Because the Communion service is less than the Mass. Such a person has already received once that day and a Communion service is meant to be for those who are unable to attend a full Mass. That’s the reason for saying that the 2nd time must be at a full Mass.