You're correct...But,
GlueBall,
Everything you say makes sense...only one problem: The U.S. Federal Air Regulations don't give a #$$% about any of this. To put it another way, the U.S. Federal Air Regulations (with regard to logging flight time) do not address this issue.
To be succinct, if a pilot is acting as the manipulator of the controls, and he/she is appropriately rated in that aircraft, then he/she may log such time as pilot in command.
The U.S. Federal Air Regulations (again, with regard to logging flight time) do not address airline seniority, what to do when two captains are flying together, who is the more experienced pilot, which pilot the airline designates (and pays) as captain.....None of these issues is addressed in the regulations. Maybe they should be, but they're not.
This issue has been cussed, discussed at length in the U.S. Obviously, the rules are different in other parts of the world, and obvioulsy the heated discussions (which have been settled years ago) have not been heard outside the borders of the U.S.
Fly safe,
PantLoad