I called the Long Beach FSDO about this two weeks ago. Except for currrency requirements and time required in pursuit of ratings your log book is yours to keep as you want. That being said, the FAA expects a pilot flying as a first officer on an aircraft in which he holds an unrestricted type rating on to log the time that he is the sole manipulator of the controls as PIC. In reading the regulation, it is unambiguous. An ailrine can weigh the time as they choose, but there are hundreds of American pilots flying in Asia as Captains that were formally first officers flying in the US.
(e) Logging pilot-in-command flight time. (1) A sport, recreational, private, commercial, or airline transport pilot may log pilot in command flight time for flights-
(i) When the pilot is the sole manipulator of the controls of an aircraft for which the pilot is rated, or has sport pilot privileges for that category and class of aircraft, if the aircraft class rating is appropriate;
(ii) When the pilot is the sole occupant in the aircraft;
(iii) When the pilot, except for a holder of a sport or recreational pilot certificate, acts as pilot in command of an aircraft for which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted; or
(iv) When the pilot performs the duties of pilot in command while under the supervision of a qualified pilot in command provided—
(A) The pilot performing the duties of pilot in command holds a commercial or airline transport pilot certificate and aircraft rating that is appropriate to the category and class of aircraft being flown, if a class rating is appropriate;