Yes, you are missing something. There is no such thing as copilot on an aircraft that is certificated as single pilot. That regulation refers to multi-crew aircraft.
On a single pilot aircraft (except when flying with an instructor or examiner) at any point in time one person only is PIC and anyone else is a passenger and nothing more. There is nothing to prevent roles being swapped at some point or for the PIC to permit the passenger to handle the controls, whilst the PIC still retains overall responsibility for the aircraft.
What cannot happen, is for two or more people to be logging time simultaneously. On a single pilot aircraft you cannot have more than one person claiming and logging any unit of time.